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<Startup-Code startupcode="########################################################### INIT #####################################################################\012\012restart:\012\012######################################################## ANIMATIOII ##################################################################\012\012AnimationII := module()                                                                                     \012\012  uses     plots, LinearAlgebra, ImageTools; \012  export   V_V, V_F, F_V, F_F, A_R, A_L, B_R, B_L, C_NN, C_NR, U_NN, U_NR, I_01, I_02, I_03,\012            b_0, b_1, B_0, B_1, B_00, B_01, B_10, B_11, B_000, B_100, B_010, B_001, B_110, \012            B_101, B_011, B_111, EP2D, EP3D, VO, VOp, D_2, OPT3D, VOE2D, VOE3D, VOF2D, VOF3D, \012           n2L, n2l, n2c, DER, BOOL, t2i, i2t, i2i, T2I, FCPM, fcpm, LAB, lab, col, COLV, NB, stdRG, \012            stdINT, M2L, L2M, I2R, V2L, C2V, RElist1, RElist2,\012            LengthTable, Indices, Tab, Purger, SearchAllInTable, MergeTable, DeleteAllInList,\012            Echanger, PreOrd, Ord, LexBoo, LexBoo3, LexOrd, Ordonner_d, Ordonner,\012            rand_i, rand_s, rand_a, ImageDir, ImageRec, Inverse, PrintTable, AddAll,\012                                                                                                            \012           nw_display, nw_point, nw_text, nw_line, nw_polygon, nw_rectangle, nw_circle, nw_disk, nw_ellipse,\012            nw_arrow, nw_coords, nw_curvcar, nw_curvpar, nw_fieldplot, nw_implicit, nw_inequal,\012            NW_arrow, NWD_arrow, NWE_arrow, NW_point, NW_line, NWD_line, NWE_line, NW_disk, NW_circle, \012            NW_rectangle, NW_polygon, \012            NWE_curvcar, NWE_curvpar, NWD_curvcar, NWD_curvpar, NWC_curvcar, NWC_curvpar, \012            NWC_implicit, NWE_implicit,\012           nw_point3d, nw_line3d, nw_polygon3d, nw_parallelepiped3d, nw_arrow3d, nw_coords3d, \012            nw_surfcar3d, nw_surfcar3d_domx, nw_surfcar3d_domy, \012            nw_surfcyl3d, nw_surfcyl3d_domr, nw_surfcyl3d_domt, nw_surfpar3d, \012            nw_curvpar3d, nw_implicit3d,\012            NW_arrow3d, NWD_arrow3d, NWE_arrow3d, NW_point3d, NW_line3d, NWD_line3d, NWE_line3d, NW_polygon3d,\012            NWC_curvpar3d, NWD_curvpar3d, NWE_curvpar3d, NWC_implicit3d, NWE_implicit3d,\012           nw_surfparXd, \012                                                                                                            \012           FAUNE;\012  local   Paragraphe;\012  option package;\012\012Paragraphe := &quot;Constantes &amp; Variables globales&quot;:                                                            \012\012V_V := [true,true]: V_F := [true,false]: F_V := [false,true]: F_F := [false,false]:\012A_R := [above,right]: A_L := [above,left]: B_R := [below,right]: B_L := [below,left]:\012C_NN := [constrained,none]:   C_NR := [constrained,normal]: \012U_NN := [unconstrained,none]: U_NR := [unconstrained,normal]:\012I_01 := [0,1]: I_02 := [[0,1],[0,1]]: I_03 := [[0,1],[0,1],[0,1]]: b_0 := false: b_1 := true: \012B_0 := [b_0]: B_1 := [b_1]: B_00 := [b_0,b_0]: B_10 := [b_1,b_0]: B_01 := [b_0,b_1]: B_11 := [b_1,b_1]:\012B_000 := [b_0,b_0,b_0]: B_100 := [b_1,b_0,b_0]: B_010 := [b_0,b_1,b_0]: B_001 := [b_0,b_0,b_1]: \012B_110 := [b_1,b_1,b_0]: B_101 := [b_1,b_0,b_1]: B_011 := [b_0,b_1,b_1]: B_111 := [b_1,b_1,b_1]:\012EP2D := pointplot([0,0],color=white,axes=none): EP3D := pointplot3d([0,0,0],color=white,axes=none):\012D_2 := [2,nul]: OPT3D := [none,0]: VO := table(): VOp := p -&gt; [seq( VO, k=1..p )]: \012VOE2D := table([ &quot;b&quot;=F_F,&quot;v&quot;=default,&quot;m&quot;=C_NR,&quot;d&quot;=D_2,&quot;j&quot;=&quot;E&quot; ]):\012VOE3D := table([ &quot;b&quot;=F_F,&quot;v&quot;=default,&quot;m&quot;=C_NR,&quot;d&quot;=[3,[45,45]],&quot;j&quot;=&quot;E&quot;,&quot;l&quot;=light1,&quot;t&quot;=0 ]):\012VOF2D := table([ &quot;b&quot;=F_F,&quot;v&quot;=default,&quot;m&quot;=C_NR,&quot;d&quot;=D_2,&quot;j&quot;=&quot;F&quot; ]):\012VOF3D := table([ &quot;b&quot;=F_F,&quot;v&quot;=default,&quot;m&quot;=C_NR,&quot;d&quot;=[3,[45,45]],&quot;j&quot;=&quot;F&quot;,&quot;l&quot;=light1,&quot;t&quot;=0 ]):\012\012Paragraphe := &quot;Routines&quot;:                                                                                   \012\012n2L    := n_                 -&gt; convert(StringTools[Char](65+n_),name):\012n2l    := n_                 -&gt; convert(StringTools[Char](32+n_),name):\012n2c    := n_                 -&gt; convert(StringTools[Char](48+n_),name):\012DER    := L_                 -&gt; L_[nops(L_)]:\012BOOL   := b_                 -&gt; ceil(evalhf(b_)):\012t2i    := (I_,t_)            -&gt; (I_[2]-I_[1])*t_+I_[1]:\012i2t    := (I_,t_)            -&gt; if I_[1]=I_[2] then 0 else (t_-I_[1])/(I_[2]-I_[1]) end if:\012i2i    := (I1_,I2_,t_)       -&gt; t2i(I2_,i2t(I1_,t_)):\012T2I    := (II_,T_)           -&gt; [seq(t2i(II_[k__],T_[k__]),k__=1..nops(II_))]:\012FCPM   := (t_,a_,b_,c_)      -&gt; a_*(1-ceil(t_))+b_*(-floor(t_)+ceil(t_))+c_*floor(t_):\012fcpm   := (I_,t_,a_,b_,c_)   -&gt; FCPM(i2t(I_,t_),a_,b_,c_):\012LAB    := (I_,t_,f_,o_)      -&gt; fcpm(I_,t_,f_(I_[1]),f_(o_),f_(I_[2])):\012lab    := (I1_,I2_,t_,f_,o_) -&gt; fcpm(I1_,t_,f_(I2_[1]),f_(o_),f_(I2_[2])):\012col    := (n_,k_)            -&gt; COLOR(RGB,(k_ mod n_)/n_,(k_+1 mod n_)/n_,(k_+2 mod n_)/n_):\012COLV    := (n_,V_)           -&gt; COLOR(RGB,(floor(V_[1]) mod n_)/n_,(floor(V_[2]) mod n_)/n_,(floor(V_[3]) mod n_)/n_):\012NB     := name_              -&gt; convert(StringTools[Select](StringTools[IsDigit],name_),decimal,10):\012stdRG  := (d_,v_)            -&gt; [seq(-v_..v_,k__=1..d_)]:\012stdINT := (d_,v_)            -&gt; if d_=1 then [-v_,v_] else [seq([-v_,v_],k__=1..d_)] end if:\012M2L    := A_                 -&gt; [seq( Column(A_,j__) , j__=1..ColumnDimension(A_) )]:\012L2M    := LL_                -&gt; convert(LL_,Matrix)^%T:\012I2R    := II_                -&gt; \012 if type(II_,listlist) then [seq(II_[k__][1]..II_[k__][2],k__=1..nops(II_))]\012                       else II_[1]..II_[2]\012                       end if:\012V2L    := V_                 -&gt; convert(V_,list):\012C2V    := z                  -&gt; &lt;Re(z),Im(z)&gt;:\012                                                                                                            \012LengthTable := tab -&gt; nops([indices(tab)]):\012Indices := proc(T_) local ind__,k__,T__:\012 if type(T_,list) then T__ := convert(T_,table) else T__ := T_ end if:\012 ind__ := []:\012 for k__ in indices(T__) do \012  if nops(k__)=1 then ind__ := [op(ind__),op(k__)] \012                 else ind__ := [op(ind__),k__] \012  end if end do:\012 ind__:\012 end proc:\012Tab := proc(T_,l_:=NULL,k_:=NULL,ij_:=NULL) local res__:\012 res__ := T_:\012 if ((type(T_,'table') or type(T_,Matrix)) or (type(T_,Vector) or type(T_,list)))\012  then  if ij_&lt;&gt;NULL then res__ := T_[op(l_)][op(k_)][op(ij_)] \012   else if k_&lt;&gt;NULL  then res__ := T_[op(l_)][op(k_)] \012   else if l_&lt;&gt;NULL  then res__ := T_[op(l_)] \012   end if end if end if\012  end if:\012 res__:\012 end proc:\012Purger := proc(II_,symb_) local II__,k__:\012 II__ := []:\012 for k__ from 1 to nops(II_) do\012  if II_[k__][1]&lt;&gt;symb_  then II__ := [op(II__),II_[k__]] end if:\012  end do:\012 II__:\012 end proc:\012SearchAllInTable := proc(elt_,L_) local Ind__,k__:\012 Ind__ := []:\012 for k__ in Indices(L_) do\012  if L_[op(k__)]=elt_ then Ind__ := [op(Ind__),k__] end if:\012  end do:\012 Ind__:\012 end proc:\012MergeTable  := proc(Vo_,Vs_) local tab__,k__:\012 tab__ := Vo_:\012 for k__ in Indices(Vs_) do tab__[op(k__)] := Vs_[op(k__)] end do:\012 op(tab__):\012 end proc:\012DeleteAllInList := proc(elt_,L_) local L__,k__:\012 L__ := []:\012 for k__ in L_ do\012  if k__&lt;&gt;elt_ then L__ := [op(L__),k__] end if:\012  end do:\012 L__:\012 end proc:\012Echanger := proc(L_,i_,j_) local tamp__,LL__:\012 LL__ := L_:\012 tamp__ := LL__[i_]: LL__[i_] := LL__[j_]: LL__[j_] := tamp__:\012 LL__:\012 end proc:\012PreOrd := proc(L_,k_,i_) local j__,L__:\012 L__ := L_:\012 for j__ from i_ to nops(L__) do \012  if evalf(L__[j__][k_])&gt;evalf(L__[i_][k_]) then L__ := Echanger(L__,i_,j__) end if:\012  end do:\012 L__:\012 end proc:\012Ord := proc(L_,k_,sens_) local i__,L__:\012 L__ := L_:\012 for i__ from 1 to nops(L__) do L__ := PreOrd(L__,k_,i__) end do:\012 if sens_=&quot;&gt;&quot; then L__ else ListTools:-Reverse(L__) end if:\012 end proc:\012LexBoo := proc(u_,v_,k_) local u__,v__,boo__,k__:\012 boo__ := true:\012 u__ := evalf(u_): v__ := evalf(v_):\012 for k__ from 1 to k_-1 do\012  boo__ := boo__ and evalb(u__[k__]=v__[k__]):\012  end do:\012 boo__ := boo__ and evalb(u__[k_]&lt;=v__[k_]):\012 not(boo__):\012 end proc:\012LexBoo3 := [(u_,v_) -&gt; LexBoo(u_,v_,1),(u_,v_) -&gt; LexBoo(u_,v_,2),(u_,v_) -&gt; LexBoo(u_,v_,3)]:\012LexOrd := proc(L_,k_,sens_) local kmin__,L__,k__:\012 kmin__ := min(k_,nops(V2L(L_[1]))):\012 L__ := L_:\012 for k__ from 1 to kmin__ do L__ := sort(L__,LexBoo3[k__]) end do:\012 if sens_=&quot;&gt;&quot; then L__ else ListTools:-Reverse(L__) end if:\012 end proc:\012Ordonner_d := proc(L_,i_) local j__,LL__:\012 LL__ := L_:\012 for j__ from i_ to nops(LL__) do \012  if LL__[j__][2]&gt;LL__[i_][2] then LL__ := Echanger(LL__,i_,j__) end if:\012  end do:\012 LL__:\012 end proc:\012Ordonner := proc(L_,sens_) local i__,LL__:\012 LL__ := L_:\012 for i__ from 1 to nops(LL__) do LL__ := Ordonner_d(LL__,i__) end do:\012 if sens_=&quot;c&quot; then LL__ := ListTools:-Reverse(LL__) end if:\012 LL__:\012 end proc:\012rand_i := proc(E_,F_) local F__,x__,y__,f__:\012 F__ := F_: f__ := table([]):\012 if nops(E_)&gt;nops(F_) then return [] end if:\012 for x__ in E_ do\012  y__ := RandomTools[Generate](choose(F__)):\012  f__[x__] := y__:\012  F__ := F__ minus {y__}:\012  end do:\012 f__:\012 end proc:\012rand_s := proc(E_,F_) local E__,x__,y__,f__:\012 E__ := E_: f__ := table([]):\012 if nops(E_)&lt;nops(F_) then return [] end if:\012 for y__ in F_ do\012  x__ := RandomTools[Generate](choose(E__)):\012  f__[x__] := y__:\012  E__ := E__ minus {x__}:\012  end do:\012 for x__ in E__ do\012  y__ := RandomTools[Generate](choose(F_)):\012  f__[x__] := y__:\012  end do:\012 f__:\012 end proc:\012rand_a := proc(E_,F_) local x__,y__,f__:\012 f__ := table([]):\012 for x__ in E_ do\012  y__ := RandomTools[Generate](choose(F_)):\012  f__[x__] := y__:\012  end do:\012 f__:\012 end proc:\012ImageDir := (f_,x_) -&gt; f_[x_]:\012ImageRec := (f_,y_) -&gt; SearchAllInTable(y_,f_):\012Inverse := proc(f_,E_,F_) local invf__,y__:\012 invf__ := table([ ]):\012 for y__ in F_ do invf__[y__] := ImageRec(f_,y__) end do:\012 invf__:\012 end proc:\012PrintTable := f_ -&gt; [seq( [x__,f_[x__]], x__ in Indices(f_) )]:\012AddAll := L_ -&gt; add(L_[k__],k__=1..nops(L_)):\012                                                                                                            \012RElist1 := MM_  -&gt; \012 if nops(MM_)=1 then [[MM_[1]],[MM_[1]]] \012                else [[seq( MM_[k__],k__=1..nops(MM_), 2)],[seq( MM_[k__+1],k__=1..nops(MM_), 2)]] \012                end if:\012RElist2 := MM_  -&gt; \012 if nops(MM_)=1 then [[MM_[1]],[MM_[1]]] \012                else [[seq( MM_[k__],k__=1..nops(MM_)-1) ],[seq( MM_[k__+1],k__=1..nops(MM_)-1)] ] \012                end if:\012\012Paragraphe := &quot;Outils Graphiques 2D&quot;:                                                                       \012nw_display   := G_  -&gt; plots[display](G_):\012nw_point     := proc(M_,AT_)  local G1__,G2__: \012 G1__ := plots[pointplot](M_,symbol=AT_[4],color=AT_[1]):\012 if type(AT_[3],list) then G2__ := plots[textplot]([M_[1],M_[2],'typeset'(op(AT_[2]))],color=AT_[1],align=AT_[3],font=[TIMES,roman,9])\012                      else G2__ := NULL\012                      end if:\012 plots[display]([ G1__,G2__ ]):\012 end proc:\012nw_text     := proc(M_,AT_) \012 if AT_[3]='nul' then plots[textplot]([M_[1],M_[2],'typeset'(op(AT_[2]))],color=AT_[1],font=[TIMES,AT_[4][1],AT_[4][2]])\012                 else plots[textplot]([M_[1],M_[2],'typeset'(op(AT_[2]))],color=AT_[1],font=[TIMES,AT_[4][1],AT_[4][2]],align=AT_[3])\012                 end if:\012 end proc:\012nw_line      := (MN_,AT_) -&gt; \012 plots[display](plottools[line]  (V2L(MN_[1]),V2L(MN_[2]),color=AT_[1],linestyle=AT_[3],thickness=AT_[4])):\012nw_circle    := (Cr_,AT_) -&gt; \012 plots[display](plottools[circle](V2L(Cr_[1]),Cr_[2]     ,color=AT_[1],linestyle=AT_[3],thickness=AT_[4])):\012nw_polygon   := (MM_,AT_) -&gt; \012 plots[display](plottools[polygon]([seq(V2L(MM_[k]),k=1..nops(MM_))],\012                color=AT_[1],transparency=AT_[2],linestyle=AT_[3],thickness=AT_[4])):\012nw_rectangle := (MN_,AT_) -&gt; \012 plots[display](plottools[rectangle](MN_[1],MN_[2],\012                color=AT_[1],transparency=AT_[2],linestyle=AT_[3],thickness=AT_[4])):\012nw_disk      := (Cr_,AT_) -&gt;\012 plots[display](plottools[disk](V2L(Cr_[1]),Cr_[2],\012                color=AT_[1],transparency=AT_[2],linestyle=AT_[3],thickness=AT_[4])):\012nw_ellipse   := (Cab_,AT_,boo_) -&gt; \012 plots[display](plottools[ellipse](V2L(Cab_[1]),Cab_[2],Cab_[3],color=AT_[1],transparency=AT_[2],linestyle=AT_[3],thickness=AT_[4],filled=boo_)):\012nw_arrow     := (MV_,AT_) -&gt; \012 plots[display](plots[arrow](MV_[1],[MV_[2]],shape=arrow,color=AT_[1],head_length=AT_[2],head_width=AT_[3],width=AT_[4])):\012nw_coords    := proc(Nr_,AT_) local G__,R__,C__,S__:\012 G__  := [AT_[4],AT_[4]]:\012 R__ := [seq(Nr_[2][k__][1]..Nr_[2][k__][2],k__=1..2)]:\012 C__ := [seq(col(2,k__),k__=0..1)]:\012 S__ := [AT_[3],AT_[3]]:\012 plots[display](coordplot(Nr_[1],R__,colour=C__,linestyle=S__,grid=G__)):\012 end proc:\012nw_curvcar  := proc(F_,AT_,filled_:=false,y_:=NULL) \012 if filled_ then \012  plots[display](plot(\012   F_[1](x__,y_), x__=I2R(F_[2]),\012   linestyle=AT_[3],thickness=AT_[4],labels=[x,y],discont=false,filled=[color=AT_[1],transparency=AT_[2]]))\012 else\012  plots[display](plot(\012   F_[1](x__,y_), x__=I2R(F_[2]),\012   color=AT_[1],linestyle=AT_[3],thickness=AT_[4],labels=[x,y],discont=false))\012 end if:\012 end proc:\012nw_curvpar := proc(F_,AT_,v_:=NULL) \012 plots[display](plot(\012   [op(V2L(F_[1](u__,v_))), u__=I2R(F_[2])],\012   color=AT_[1],linestyle=AT_[3],thickness=AT_[4],labels=[x,y],discont=false)):\012 end proc:\012nw_fieldplot := proc(F_,AT_)\012 plots[display](plots[fieldplot](\012   V2L(F_[1](x__,y__)),x__=I2R(F_[2][1]),y__=I2R(F_[2][2]),\012   color=AT_[1],clipping=AT_[2],grid=AT_[3],fieldstrength=AT_[4])):\012 end proc:\012nw_implicit := proc(F_,AT_,filled_:=0,t_:=NULL)\012 if filled_=0 then \012  plots[display](plots[implicitplot](\012   F_[1](x__,y__,t_)=0,x__=I2R(F_[2][1]),y__=F_[2][2][1](x__)..F_[2][2][2](x__),\012   color=AT_[1],gridrefine=AT_[2],linestyle=AT_[3],thickness=AT_[4]))\012 else if filled_=1 then\012  plots[display](plots[implicitplot](\012   F_[1](x__,y__,t_)=0,x__=I2R(F_[2][1]),y__=F_[2][2][1](x__)..F_[2][2][2](x__),\012   coloring=AT_[1],gridrefine=AT_[2],grid=AT_[3],transparency=AT_[4],\012   filledregions))\012 else if filled_=2 then\012  plots[display](plots[implicitplot](\012   F_[1](x__,y__,t_)&lt;=0,x__=I2R(F_[2][1]),y__=F_[2][2][1](x__)..F_[2][2][2](x__),\012   coloring=AT_[1],gridrefine=AT_[2],grid=AT_[3],transparency=AT_[4],\012   filledregions))\012 end if end if end if:\012 end proc:\012nw_inequal := proc(F_,AT_,boo_:=true,t_:=NULL)\012 if boo_ then \012  plots[display](plots[inequal](\012   F_[1](x__,y__,t_),x__=I2R(F_[2][1]),y__=I2R(F_[2][2]),\012   'optionsfeasible'=[seq( [color=AT_[1][1][k__],transparency=AT_[1][2]], k__=1..nops(AT_[1][1]) )],\012   'optionsexcluded'=[color=AT_[2][1],transparency=AT_[2][2]],\012   'optionsclosed'=[color=AT_[3][1],thickness=AT_[3][2]],\012   'optionsimplicit'=[gridrefine=AT_[4]] ))\012 else\012  plots[display](plots[inequal](\012   F_[1](x__,y__,t_),x__=I2R(F_[2][1]),y__=I2R(F_[2][2]),\012   'optionsfeasible'=[seq( [color=AT_[1][1][k__],transparency=AT_[1][2]], k__=1..nops(AT_[1][1]) )],\012   'optionsexcluded'=[color=AT_[2][1],transparency=AT_[2][2]],\012   'optionsclosed'=[color=AT_[3][1],thickness=AT_[3][2]],\012   'optionsimplicit'=[gridrefine=AT_[4]],\012   'nolines' ))\012 end if:\012 end proc:\012\012                                                                                                            \012NWC_curvcar  := proc(FF_,AT_,filled_:=false,y_:=NULL) \012 if type(AT_,listlist) \012  then plots[display]([ seq( nw_curvcar([FF_[1][k__],FF_[2]],AT_[k__],filled_,y_) , k__=1..nops(FF_[1]) ) ])\012  else plots[display]([ seq( nw_curvcar([FF_[1][k__],FF_[2]],AT_,filled_,y_)      , k__=1..nops(FF_[1]) ) ])\012  end if:\012 end proc:\012NWD_curvcar  := proc(FF_,AT_,filled_:=false,y_:=NULL) \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_curvcar([FF_[1],FF_[2][k__]],AT_[k__],filled_,y_) , k__=1..nops(FF_[2]) ) ])\012  else plots[display]([ seq( nw_curvcar([FF_[1],FF_[2][k__]],AT_,filled_,y_)      , k__=1..nops(FF_[2]) ) ])\012  end if:\012 end proc:\012NWE_curvcar := proc(FF_,AT_,filled_:=false,y_:=NULL) \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_curvcar(FF_[k__],AT_[k__],filled_,y_) , k__=1..nops(FF_) ) ])\012  else plots[display]([ seq( nw_curvcar(FF_[k__],AT_,filled_,y_)      , k__=1..nops(FF_) ) ])\012  end if:\012 end proc:\012NWC_curvpar := proc(FF_,AT_,v_:=NULL) \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_curvpar([FF_[1][k__],FF_[2]],AT_[k__],v_) , k__=1..nops(FF_[1]) ) ])\012  else plots[display]([ seq( nw_curvpar([FF_[1][k__],FF_[2]],AT_,v_)      , k__=1..nops(FF_[1]) ) ])\012  end if:\012 end proc:\012NWD_curvpar := proc(FF_,AT_,v_:=NULL) \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_curvpar([FF_[1],FF_[2][k__]],AT_[k__],v_) , k__=1..nops(FF_[2]) ) ])\012  else plots[display]([ seq( nw_curvpar([FF_[1],FF_[2][k__]],AT_,v_)      , k__=1..nops(FF_[2]) ) ])\012  end if:\012 end proc:\012NWE_curvpar := proc(FF_,AT_,v_:=NULL) \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_curvpar(FF_[k__],AT_[k__],v_) , k__=1..nops(FF_) ) ])\012  else plots[display]([ seq( nw_curvpar(FF_[k__],AT_,v_)      , k__=1..nops(FF_) ) ])\012  end if:\012 end proc:\012NW_arrow := proc(MVV_,AT_)  \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_arrow([MVV_[1],MVV_[2][k__]],AT_[k__]),k__=1..nops(MVV_[2]) ) ])\012  else plots[display]([ seq( nw_arrow([MVV_[1],MVV_[2][k__]],AT_)     ,k__=1..nops(MVV_[2]) ) ])\012  end if:\012 end proc:\012NWD_arrow := NW_arrow:\012NWE_arrow := proc(MVMV_,AT_) \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_arrow(MVMV_[k__],AT_[k__]),k__=1..nops(MVMV_) ) ])\012  else plots[display]([ seq( nw_arrow(MVMV_[k__],AT_)     ,k__=1..nops(MVMV_) ) ])\012  end if:\012 end proc:\012NW_point  := proc(MM_,AT_)  \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_point(MM_[k__],AT_[k__]),k__=1..nops(MM_) ) ])\012  else plots[display]([ seq( nw_point(MM_[k__],AT_)     ,k__=1..nops(MM_) ) ])\012  end if:\012 end proc:\012NW_line   := proc(MMNN_,AT_)\012 if type(AT_,listlist) \012  then plots[display]([ seq( nw_line([MMNN_[1][k__],MMNN_[2][k__]],AT_[k__]),k__=1..nops(MMNN_[1]) ) ])\012  else plots[display]([ seq( nw_line([MMNN_[1][k__],MMNN_[2][k__]],AT_)     ,k__=1..nops(MMNN_[1]) ) ])\012  end if:\012 end proc:\012NWD_line  := proc(MNN_,AT_)\012 if type(AT_,listlist) \012  then plots[display]([ seq( nw_line([MNN_[1],MNN_[2][k__]],AT_[k__]),k__=1..nops(MNN_[2]) ) ])\012  else plots[display]([ seq( nw_line([MNN_[1],MNN_[2][k__]],AT_)     ,k__=1..nops(MNN_[2]) ) ])\012  end if:\012 end proc:\012NWE_line  := proc(MNMN_,AT_)\012 if type(AT_,listlist) \012  then plots[display]([ seq( nw_line(MNMN_[k__],AT_[k__]),k__=1..nops(MNMN_) ) ])\012  else plots[display]([ seq( nw_line(MNMN_[k__],AT_)     ,k__=1..nops(MNMN_) ) ])\012  end if:\012 end proc:\012NW_disk := proc(CrCr_,AT_)  \012 if type(AT_,listlist) \012  then plots[display]([ seq( nw_disk(CrCr_[k__],AT_[k__]),k__=1..nops(CrCr_) ) ])\012  else plots[display]([ seq( nw_disk(CrCr_[k__],AT_)     ,k__=1..nops(CrCr_) ) ])\012  end if:\012 end proc:\012NW_circle := proc(CrCr_,AT_)  \012 if type(AT_,listlist) \012  then plots[display]([ seq( nw_circle(CrCr_[k__],AT_[k__]),k__=1..nops(CrCr_) ) ])\012  else plots[display]([ seq( nw_circle(CrCr_[k__],AT_)     ,k__=1..nops(CrCr_) ) ])\012  end if:\012 end proc:\012NW_rectangle := proc(MNMN_,AT_)  \012 if type(AT_,listlist) \012  then plots[display]([ seq( nw_rectangle(MNMN_[k__],AT_[k__]),k__=1..nops(MNMN_) ) ])\012  else plots[display]([ seq( nw_rectangle(MNMN_[k__],AT_)     ,k__=1..nops(MNMN_) ) ])\012  end if:\012 end proc:\012NW_polygon := proc(MMMM_,AT_)  \012 if type(AT_,listlist) \012  then plots[display]([ seq( nw_polygon(MMMM_[k__],AT_[k__]),k__=1..nops(MMMM_) ) ])\012  else plots[display]([ seq( nw_polygon(MMMM_[k__],AT_)     ,k__=1..nops(MMMM_) ) ])\012  end if:\012 end proc:\012NWC_implicit := proc(FF_,AT_,filled_,t_:=NULL)  \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_implicit([FF_[1][k__],FF_[2]],AT_[k__],filled_,t_) , k__=1..nops(FF_[1]) ) ])\012  else plots[display]([ seq( nw_implicit([FF_[1][k__],FF_[2]],AT_,filled_,t_)      , k__=1..nops(FF_[1]) ) ])\012  end if:\012 end proc:\012NWE_implicit := proc(FF_,AT_,filled_,t_:=NULL) \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_implicit(FF_[k__],AT_[k__],filled_,t_) , k__=1..nops(FF_) ) ])\012  else plots[display]([ seq( nw_implicit(FF_[k__],AT_,filled_,t_)      , k__=1..nops(FF_) ) ])\012  end if:\012 end proc:\012Paragraphe := &quot;Outils Graphiques 3D&quot;:                                                                      \012\012nw_point3d := (M_,AT_) -&gt; \012 plots[display]\012  ([ plots[pointplot3d](M_,symbol=AT_[4],color=AT_[1]),\012     plots[textplot3d]([M_[1],M_[2],M_[3],typeset(AT_[2])],align=AT_[3],color=AT_[1]) ]):\012nw_line3d := (MN_,AT_) -&gt; \012 plots[display](plottools[line](V2L(MN_[1]),V2L(MN_[2]),linestyle=AT_[3],color=AT_[1],thickness=AT_[4])):\012nw_polygon3d   := (MM_,AT_) -&gt; \012 plots[display](plottools[polygon]([seq(V2L(MM_[k]),k=1..nops(MM_))],color=AT_[1],transparency=AT_[2])):\012nw_parallelepiped3d   := (MM_,AT_) -&gt; \012 plots[display](plottools[parallelepiped](op(MM_)),color=AT_[1],transparency=AT_[2]):\012nw_surfcar3d  := proc(F_,AT_,w_:=NULL) local x__,y__:\012 plots[display](plot3d(\012  F_[1](x__,y__,w_), \012  x__=I2R(F_[2])[1],y__=I2R(F_[2])[2], \012  color=AT_[1],transparency=AT_[2],style=AT_[3],grid=[AT_[4],AT_[4]]),\012  labels=[x,y,z]\012  ):\012 end proc:\012nw_surfcar3d_domx  := proc(F_,AT_,w_:=NULL) local x__,y__:\012 plots[display](plot3d(\012  F_[1](x__,y__,w_), \012  x__=I2R(F_[2][1]),y__=F_[2][2][1](x__)..F_[2][2][2](x__), \012  color=AT_[1],transparency=AT_[2],style=AT_[3],grid=[AT_[4],AT_[4]]),\012  labels=[x,y,z]\012  ):\012 end proc:\012nw_surfcar3d_domy  := proc(F_,AT_,w_:=NULL) local x__,y__:\012 plots[display](plot3d(\012  F_[1](x__,y__,w_), \012  x__=F_[2][1][1](y__)..F_[2][1][2](y__),y__=I2R(F_[2][2]), \012  color=AT_[1],transparency=AT_[2],style=AT_[3],grid=[AT_[4],AT_[4]]),\012  labels=[x,y,z]\012  ):\012 end proc:\012nw_surfcyl3d  := proc(F_,AT_,w_:=NULL) local r__,t__:\012 addcoords(nw_cylindrical,[z,r,theta],[r*cos(theta),r*sin(theta),z]):\012 plots[display](plot3d(\012  F_[1](r__,t__,w_), \012  r__=I2R(F_[2])[1],t__=I2R(F_[2])[2], \012  coords=nw_cylindrical,\012  color=AT_[1],transparency=AT_[2],style=AT_[3],grid=[AT_[4],AT_[4]]),\012  labels=[x,y,z]\012  ):\012 end proc:\012nw_surfcyl3d_domr  := proc(F_,AT_,w_:=NULL) local r__,t__:\012 addcoords(nw_cylindrical,[z,r,theta],[r*cos(theta),r*sin(theta),z]):\012 plots[display](plot3d(\012  F_[1](r__,t__,w_), \012  r__=I2R(F_[2][1]),t__=F_[2][2][1](r__)..F_[2][2][2](r__), \012  coords=nw_cylindrical,\012  color=AT_[1],transparency=AT_[2],style=AT_[3],grid=[AT_[4],AT_[4]]),\012  labels=[x,y,z]\012  ):\012 end proc:\012nw_surfcyl3d_domt  := proc(F_,AT_,w_:=NULL) local r__,t__:\012 addcoords(nw_cylindrical,[z,r,theta],[r*cos(theta),r*sin(theta),z]):\012 plots[display](plot3d(\012  F_[1](r__,t__,w_), \012  r__=F_[2][1][1](t__)..F_[2][1][2](t__),t__=I2R(F_[2][2]), \012  coords=nw_cylindrical,\012  color=AT_[1],transparency=AT_[2],style=AT_[3],grid=[AT_[4],AT_[4]]),\012  labels=[x,y,z]\012  ):\012 end proc:\012nw_surfpar3d := proc(F_,AT_,w_:=NULL) local u__,v__:\012 plots[display](plot3d(\012  V2L(F_[1](u__,v__,w_)), \012  u__=I2R(F_[2])[1],v__=I2R(F_[2])[2], \012  color=AT_[1],transparency=AT_[2],style=AT_[3],grid=[AT_[4],AT_[4]],coords=rectangular),\012  labels=[x,y,z]\012  ):\012 end proc:\012nw_curvpar3d := proc(F_,AT_,v_:=NULL) local u__:\012 plots[display](plots[spacecurve](\012  V2L(F_[1](u__,v_)),\012  u__= I2R(F_[2]),\012  color=AT_[1],linestyle=AT_[3],thickness=AT_[4])):\012 end proc:\012nw_arrow3d     := (MV_,AT_)   -&gt;\012 plots[display]\012  ([ plottools[line](V2L(MV_[1]),V2L(MV_[1]+MV_[2]),color=AT_[1],linestyle=AT_[3],thickness=AT_[4]),\012     plottools[point](V2L(MV_[1]+MV_[2]),color=AT_[1],symbol=solidsphere) ]):\012nw_coords3d := proc(Nr_,AT_) local G__,R__,V__,C__,S__:\012 G__ := [AT_[4],AT_[4]]:\012 R__ := I2R(Nr_[2]):\012 V__ := stdRG(3,1):\012 C__ := [seq(col(3,k__),k__=0..2)]:\012 S__ := AT_[3]:\012 coordplot3d(Nr_[1],R__,colour=C__,style=S__,grid=G__,view=V__):\012 end proc:\012nw_implicit3d := proc(F_,AT_,t_:=NULL)\012 plots[implicitplot3d](\012   F_[1](x__,y__,z__,t_),x__=I2R(F_[2][1]),y__=I2R(F_[2][2]),z__=I2R(F_[2][3]),\012   color=AT_[1],transparency=AT_[2],style=AT_[3],grid=AT_[4],labels=[&quot;&quot;,&quot;&quot;,&quot;&quot;]):\012 end proc:\012\012Paragraphe := &quot;Outils Graphiques XD&quot;:                                                                      \012\012nw_surfparXd := proc(F_,AT_,w_:=NULL) local u__,v__:\012 plots[display](plot3d(\012  V2L(F_[1]([u__,v__],w_)), \012  u__=I2R(F_[2])[1],v__=I2R(F_[2])[2], \012  color=AT_[1],transparency=AT_[2],style=AT_[3],grid=[AT_[4],AT_[4]],coords=rectangular),\012  labels=[x,y,z]\012  ):\012 end proc:\012                                                                                                            \012NWC_curvpar3d := proc(FF_,AT_,v_:=NULL) \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_curvpar3d([FF_[1][k__],FF_[2]],AT_[k__],v_) , k__=1..nops(FF_[1]) ) ])\012  else plots[display]([ seq( nw_curvpar3d([FF_[1][k__],FF_[2]],AT_,v_)      , k__=1..nops(FF_[1]) ) ])\012  end if:\012 end proc:\012NWD_curvpar3d := proc(FF_,AT_,v_:=NULL) \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_curvpar3d([FF_[1],FF_[2][k__]],AT_[k__],v_) , k__=1..nops(FF_[2]) ) ])\012  else plots[display]([ seq( nw_curvpar3d([FF_[1],FF_[2][k__]],AT_,v_)      , k__=1..nops(FF_[2]) ) ])\012  end if:\012 end proc:\012NWE_curvpar3d := proc(FF_,AT_,v_:=NULL) \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_curvpar3d(FF_[k__],AT_[k__],v_) , k__=1..nops(FF_) ) ])\012  else plots[display]([ seq( nw_curvpar3d(FF_[k__],AT_,v_)      , k__=1..nops(FF_) ) ])\012  end if:\012 end proc:\012NW_arrow3d := proc(MVV_,AT_)  \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_arrow3d([MVV_[1],MVV_[2][k__]],AT_[k__]),k__=1..nops(MVV_[2]) ) ])\012  else plots[display]([ seq( nw_arrow3d([MVV_[1],MVV_[2][k__]],AT_)     ,k__=1..nops(MVV_[2]) ) ])\012  end if:\012 end proc:\012NWD_arrow3d := NW_arrow3d:\012NWE_arrow3d := proc(MVMV_,AT_) \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_arrow3d(MVMV_[k__],AT_[k__]),k__=1..nops(MVMV_) ) ])\012  else plots[display]([ seq( nw_arrow3d(MVMV_[k__],AT_)     ,k__=1..nops(MVMV_) ) ])\012  end if:\012 end proc:\012NW_point3d  := proc(MM_,AT_)  \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_point3d(MM_[k__],AT_[k__]),k__=1..nops(MM_) ) ])\012  else plots[display]([ seq( nw_point3d(MM_[k__],AT_)     ,k__=1..nops(MM_) ) ])\012  end if:\012 end proc:\012NW_line3d   := proc(MMNN_,AT_)\012 if type(AT_,listlist) \012  then plots[display]([ seq( nw_line3d([MMNN_[1][k__],MMNN_[2][k__]],AT_[k__]),k__=1..nops(MMNN_[1]) ) ])\012  else plots[display]([ seq( nw_line3d([MMNN_[1][k__],MMNN_[2][k__]],AT_)     ,k__=1..nops(MMNN_[1]) ) ])\012  end if:\012 end proc:\012NWD_line3d  := proc(MNN_,AT_)\012 if type(AT_,listlist) \012  then plots[display]([ seq( nw_line3d([MNN_[1],MNN_[2][k__]],AT_[k__]),k__=1..nops(MNN_[2]) ) ])\012  else plots[display]([ seq( nw_line3d([MNN_[1],MNN_[2][k__]],AT_)     ,k__=1..nops(MNN_[2]) ) ])\012  end if:\012 end proc:\012NWE_line3d  := proc(MNMN_,AT_)\012 if type(AT_,listlist) \012  then plots[display]([ seq( nw_line3d(MNMN_[k__],AT_[k__]),k__=1..nops(MNMN_) ) ])\012  else plots[display]([ seq( nw_line3d(MNMN_[k__],AT_)     ,k__=1..nops(MNMN_) ) ])\012  end if:\012 end proc:\012NW_polygon3d   := (MMMM_,AT_) -&gt;  \012 plots[display]([seq( nw_polygon3d(MMMM_[k__],AT_),k__=1..nops(MMMM_))]):\012NWC_implicit3d := proc(FF_,AT_,t_:=NULL)  \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_implicit3d([FF_[1][k__],FF_[2]],AT_[k__],t_) , k__=1..nops(FF_[1]) ) ])\012  else plots[display]([ seq( nw_implicit3d([FF_[1][k__],FF_[2]],AT_,t_)      , k__=1..nops(FF_[1]) ) ])\012  end if:\012 end proc:\012NWE_implicit3d := proc(FF_,AT_,t_:=NULL) \012 if type(AT_,listlist)\012  then plots[display]([ seq( nw_implicit3d(FF_[k__],AT_[k__],t_) , k__=1..nops(FF_) ) ])\012  else plots[display]([ seq( nw_implicit3d(FF_[k__],AT_,t_)      , k__=1..nops(FF_) ) ])\012  end if:\012 end proc:\012\012                                                                                                            \012\012FAUNE := proc() local img:\012 img := Read(cat(savelibname,&quot;\134\134faune.jpg&quot;)):\012 img := GetSubImage(img,1,1,4300,3672):\012 img := Scale(img,0.1):\012 img := Preview(img):\012 end proc:\012\012end module:                                                                                                 \012                                                                                                                                    \012                                                                                                            \012######################################################### ALGLIN ###################################################################\012\012AlgLin := module()                                                                                          \012\012  uses     plots, LinearAlgebra, AnimationII; \012  export   O_2, O_3, EMAT, EVEC,\012           ID2, ROT2,REF2,PROJ2_VD, DIL2_VD, REF2_VD, id, hom, trans, rot2, ref2, proj2_vd, dil2_vd, \012             ref2_vd, Id, Hom, Trans, Rot2, Ref2, Proj2_vd, Dil2_vd, Ref2_vd, \012             MinusVect, AugmentMatrix, AugmentVector, Famille, BaseCan, \012             FindOrtho2d, FindOrtho3d, Orthogonal2d, Orthogonal3d, OrthoDec, Ker, Img, Vs_Param, DetVect, \012             EigenSpaceReal, EigenAngles2d,\012           ID3, ROT3,PROJ3_VD, PROJ3_VN, DIL3_VN, REF3_VN, ANTISYM3, rot3, proj3_vd, proj3_vn, dil3_vn,  \012             ref3_vn, Rot3, Proj3_vn, Dil3_vn, Ref3_vn, Cercle3d, Angles3d, Pol, Spheric;\012  local    Paragraphe;\012  option package;\012\012Paragraphe := &quot;Constantes &amp; Variables globales&quot;:                                                            \012\012O_2  := &lt;0,0&gt;: O_3 := &lt;0,0,0&gt;:\012EMAT   := (n,p) -&gt; Matrix(n,p,(i,j)-&gt;NULL):\012EVEC   := n -&gt; Vector(n,i-&gt;NULL):\012\012 Paragraphe := &quot;Alg\303\250bre Lin\303\251aire&quot;:                                                                          \012\012ID2      :=         IdentityMatrix(2):\012ROT2     := t_      -&gt; &lt;&lt;cos(t_),sin(t_)&gt;|&lt;-sin(t_),cos(t_)&gt;&gt;:\012REF2     := t_      -&gt; &lt;&lt;cos(t_),sin(t_)&gt;|&lt;sin(t_),-cos(t_)&gt;&gt;:\012PROJ2_VD := a_      -&gt; (1/(a_^%T.a_))*(a_.a_^%T):\012DIL2_VD  := (a_,k_) -&gt; k_*ID2+(1-k_)*PROJ2_VD(a_):\012REF2_VD  := a_      -&gt; -ID2+2*PROJ2_VD(a_):\012                                                                                                            \012id       := M_            -&gt; M_:\012hom      := (I_,a_,k_,M_) -&gt; evalf(I_+k_            *(M_-I_)):\012trans    := (I_,a_,k_,M_) -&gt; evalf(M_+a_):\012rot2     := (I_,a_,k_,M_) -&gt; evalf(I_+ROT2(k_)      .(M_-I_)):\012ref2     := (I_,a_,k_,M_) -&gt; evalf(I_+REF2(k_)      .(M_-I_)):\012proj2_vd := (I_,a_,k_,M_) -&gt; evalf(I_+PROJ2_VD(a_)  .(M_-I_)):\012dil2_vd  := (I_,a_,k_,M_) -&gt; evalf(I_+DIL2_VD(a_,k_).(M_-I_)):\012ref2_vd  := (I_,a_,k_,M_) -&gt; evalf(I_+REF2_VD(a_)   .(M_-I_)):\012                                                                                                            \012Id       := MM_            -&gt; MM_:\012Hom      := (I_,a_,k_,MM_) -&gt; map[4](hom     ,I_,a_,k_,MM_):\012Trans    := (I_,a_,k_,MM_) -&gt; map[4](trans   ,I_,a_,k_,MM_):\012Rot2     := (I_,a_,k_,MM_) -&gt; map[4](rot2    ,I_,a_,k_,MM_):\012Ref2     := (I_,a_,k_,MM_) -&gt; map[4](ref2    ,I_,a_,k_,MM_):\012Proj2_vd := (I_,a_,k_,MM_) -&gt; map[4](proj2_vd,I_,a_,k_,MM_):\012Dil2_vd  := (I_,a_,k_,MM_) -&gt; map[4](dil2_vd ,I_,a_,k_,MM_):\012Ref2_vd  := (I_,a_,k_,MM_) -&gt; map[4](ref2_vd ,I_,a_,k_,MM_):\012                                                                                                            \012ID3      :=         IdentityMatrix(3):\012PROJ3_VD := a_      -&gt; (1/(a_^%T.a_))*(a_.a_^%T):\012PROJ3_VN := a_      -&gt; ID3-PROJ3_VD(a_):\012DIL3_VN  := (a_,k_) -&gt; ID3-(1-k_)*PROJ3_VD(a_):\012REF3_VN  := a_      -&gt; ID3-2*PROJ3_VD(a_):\012ANTISYM3 := a_      -&gt; &lt;&lt;0,a_[3],-a_[2]&gt;|&lt;-a_[3],0,a_[1]&gt;|&lt;a_[2],-a_[1],0&gt;&gt;:\012ROT3     := (a_,t_) -&gt; cos(t_)*PROJ3_VN(a_)+(ID3-PROJ3_VN(a_))+sin(t_)*ANTISYM3(Normalize(a_,2)):\012                                                                                                            \012rot3     := (I_,a_,k_,M_)  -&gt; evalf(I_+ROT3(a_,k_)   .(M_-I_)):\012proj3_vd := (I_,a_,k_,M_)  -&gt; evalf(I_+PROJ3_VD(a_)  .(M_-I_)):\012proj3_vn := (I_,a_,k_,M_)  -&gt; evalf(I_+PROJ3_VN(a_)  .(M_-I_)):\012dil3_vn  := (I_,a_,k_,M_)  -&gt; evalf(I_+DIL3_VN(a_,k_).(M_-I_)):\012ref3_vn  := (I_,a_,k_,M_)  -&gt; evalf(I_+REF3_VN(a_)   .(M_-I_)):\012\012Rot3     := (I_,a_,k_,MM_) -&gt; map[4](rot3    ,I_,a_,k_,MM_):\012Proj3_vn := (I_,a_,k_,MM_) -&gt; map[4](proj3_vn,I_,a_,k_,MM_):\012Dil3_vn  := (I_,a_,k_,MM_) -&gt; map[4](dil3_vn ,I_,a_,k_,MM_):\012Ref3_vn  := (I_,a_,k_,MM_) -&gt; map[4](ref3_vn ,I_,a_,k_,MM_):\012                                                                                                            \012MinusVect := proc(LV1,LV2) local L,v1,v2,b:\012 L := []: \012 for v1 in LV1 do\012  b := 0:\012  for v2 in LV2 do if Equal(v2,v1) then b := 1 end if: end do:\012  if b=0 then L := [op(L),v1] end if:\012  end do:\012 L:\012 end proc:\012AugmentMatrix := proc(A_,n_,p_) local A__:\012 A__ := Matrix(n_,p_):\012 A__[1..RowDimension(A_),1..ColumnDimension(A_)] := A_:\012 A__:\012 end proc:\012AugmentVector := proc(VV_,n_,p_) local A__:\012 A__ := Matrix(n_,p_):\012 A__[1..Dimension(VV_[1]),1..nops(VV_)] := convert(VV_,Matrix):\012 [seq(Column(A__,k__),k__=1..ColumnDimension(A__))]:\012 end proc:\012Famille  := proc(VV_) local libre__,liee__:\012 libre__ := Basis(VV_):\012 liee__ := convert(`minus`(convert(VV_,set),convert(libre__,set)),list):\012 [libre__,liee__]:\012 end proc:\012BaseCan  := n_ -&gt; [seq(UnitVector(k__,n_),k__=1..n_)]:\012FindOrtho2d := V_ -&gt; &lt;-V_[2],V_[1]&gt;:\012FindOrtho3d := proc(V_) local U__:\012 U__ := &lt;-V_[3],0,V_[1]&gt;:\012 if Equal(U__,&lt;0,0,0&gt;) then U__ := &lt;0,-V_[3],V_[2]&gt; end if:\012 U__:\012 end proc:\012Orthogonal2d := proc(VS_) local VO__:\012 if (nops(VS_)=1 and VS_=[&lt;0,0&gt;]) then VO__ := BaseCan(2):\012  else if nops(VS_)=1             then VO__ := [FindOrtho2d(VS_[1])]:\012  else if nops(VS_)=2             then VO__ := [&lt;0,0&gt;]:\012  end if end if end if: \012 VO__:\012 end proc:\012Orthogonal3d := proc(VS_) local U1__,VO__:\012 if (nops(VS_)=1 and Equal(VS_[1],&lt;0,0,0&gt;)) then VO__ := BaseCan(3):\012  else if nops(VS_)=1                       then U1__ := FindOrtho3d(VS_[1]): \012                                                 VO__ := [U1__,CrossProduct(VS_[1],U1__)]: \012  else if nops(VS_)=2                       then VO__ := [CrossProduct(VS_[1],VS_[2])]:\012  else if nops(VS_)=3                       then VO__ := [&lt;0,0,0&gt;]\012  end if end if end if end if:\012 VO__:\012 end proc:\012OrthoDec := proc(VS_,X_) local X1__:\012 if nops(VS_)=1       then X1__ := DotProduct(VS_[1],X_)*VS_[1]: \012  else if nops(VS_)=2 then X1__ := DotProduct(VS_[1],X_)*VS_[1]+DotProduct(VS_[2],X_)*VS_[2]:\012  else if nops(VS_)=3 then X1__ := X_:\012  end if end if end if:\012 [X1__,X_-X1__]:\012 end proc:\012Ker := A_ -&gt; LexOrd(convert(NullSpace(A_)  ,list),3,&quot;&lt;&quot;): \012Img := A_ -&gt; LexOrd(convert(ColumnSpace(A_),list),3,&quot;&lt;&quot;): \012DetVect  := VV_ -&gt; Determinant(convert(VV_,Matrix)):\012EigenSpaceReal := proc(A_) local eigenvectors__,eigenspaces__,k__:\012 eigenvectors__ := Eigenvectors(A_,output='list'):\012 eigenspaces__  := []:\012 for k__ from 1 to nops(eigenvectors__) do\012  if Im(eigenvectors__[k__][1])=0 then \012   eigenspaces__ := [op(eigenspaces__),eigenvectors__[k__]]\012   end if:\012  end do:\012 for k__ from 1 to nops(eigenspaces__) do eigenspaces__[k__][3] := LexOrd(convert(eigenspaces__[k__][3],list),3,&quot;&lt;&quot;) end do:\012 Ord(eigenspaces__,1,&quot;&lt;&quot;):\012 end proc:\012EigenAngles2d := proc(eigenspaces_) local angles__,k__,l__,esk__:\012 angles__ := []:\012 for k__ from 1 to nops(eigenspaces_) do \012  esk__ := eigenspaces_[k__]:\012  angles__ := [ op(angles__),\012                   seq( [esk__[1],evalf(argument( esk__[3][l__][1]+I*esk__[3][l__][2]))], l__=1..nops(esk__[3]) ),\012                   seq( [esk__[1],evalf(argument(-esk__[3][l__][1]-I*esk__[3][l__][2]))], l__=1..nops(esk__[3]) ) ]:\012 \012  end do:\012 Ord(angles__,2,&quot;&lt;&quot;):\012 end proc:\012                                                                                                            \012Vs_Param  := proc(VS_,t_) local res__:\012 if nops(VS_)=1       then res__ := t_*VS_[1]\012  else if nops(VS_)=2 then res__ := t_[1]*VS_[1]+t_[2]*VS_[2]\012  else if nops(VS_)=3 then res__ := t_[1]*VS_[1]+t_[2]*VS_[2]+t_[3]*VS_[3]\012  end if end if end if:\012 res__:\012 end proc:\012Cercle3d := proc(I_,a_,t_) local P__,ImP__:\012 P__ := PROJ3_VN(a_):\012 ImP__ := GramSchmidt(ColumnSpace(P__),normalized,conjugate=false):\012 I_+ImP__[1]*cos(t_)+ImP__[2]*sin(t_):\012 end proc:\012Cercle3d := proc(I_,a_,t_) local a__,b__,c__:\012 a__ := Normalize(a_,Euclidean):\012 b__ := Normalize(FindOrtho3d(a__),Euclidean):\012 c__ := CrossProduct(a__,b__):\012 I_+b__*cos(t_)+c__*sin(t_):\012 end proc:\012Angles3d := proc(u) local spheric:\012 spheric := u -&gt; map(evalf,Student[VectorCalculus][MapToBasis](u,spherical)):\012 map(evalf,[spheric(u)[3]*180/Pi,spheric(u)[2]*180/Pi,0]):\012 end proc:\012Pol     := (r_,theta_) -&gt; &lt;r_*cos(theta_),r_*sin(theta_)&gt;:\012Spheric := (r_,theta_,phi_) -&gt; &lt;r_*cos(theta_)*sin(phi_),r_*sin(theta_)*sin(phi_),r_*cos(phi_)&gt;:\012\012end module:                                                                            \012                                                                                                            \012######################################################## ANALYSE ##################################################################\012\012Analyse := module()                                                                                         \012\012  uses     plots, LinearAlgebra, AnimationII; \012  export   Comp1, DD, dd, dd2, dd3, Om, Om3, Img1, Img2, View_p, ImDom, Recup, IIRecup, lim, Approx,\012           Comp2, DDP, ddp, ddp2,ddp3;\012  local    Paragraphe;\012  option package;\012\012Paragraphe := &quot;Constantes &amp; Variables globales&quot;:                                                            \012\012 Paragraphe := &quot;Analyse&quot;:                                                                                   \012Comp1  := (f_,n_)       -&gt; [seq( unapply(f_(t_)[k__],t_),k__=1..n_)]:\012DD     := (f_,n_,p_)    -&gt; map(D@@p_,Comp1(f_,n_)):\012dd     := (f_,n_,p_)    -&gt; unapply(convert(map(apply,DD(f_,n_,p_),t_),Vector),t_):\012dd2    := (f_,p_)       -&gt; dd(f_,2,p_):\012dd3    := (f_,p_)       -&gt; dd(f_,3,p_):\012Comp2  := (f_,n_)       -&gt; [seq( unapply(f_(u_,v_)[k__],u_,v_),k__=1..n_)]:\012DDP    := (f_,n_,i_,j_) -&gt; map(D[seq(1,ii__=1..i_),seq(2,jj__=1..j_)],Comp2(f_,n_)):\012ddp    := (f_,n_,i_,j_) -&gt; unapply(convert(map(apply,DDP(f_,n_,i_,j_),u_,v_),Vector),u_,v_):\012ddp2   := (f_,i_,j_) -&gt; ddp(f_,2,i_,j_):\012ddp3   := (f_,i_,j_) -&gt; ddp(f_,3,i_,j_):\012Om     := t_      -&gt; &lt;cos(t_),sin(t_)&gt;:\012Om3    := t_      -&gt; &lt;cos(t_),sin(t_),0&gt;:\012Img1   := proc(f_,II_,N_) local min__, max__: \012 min__ := evalf(min( seq( seq(f_(t2i(II_[k__],j__/N_)),j__=0..N_) , k__=1..nops(II_) ) )):\012 max__ := evalf(max( seq( seq(f_(t2i(II_[k__],j__/N_)),j__=0..N_) , k__=1..nops(II_) ) )):\012 [min__,max__]:\012 end proc:\012Img2   := proc(f_,II_,N_) local img1__, img2__:\012 img1__ := Img1(Comp1(f_,2)[1],II_,N_):\012 img2__ := Img1(Comp1(f_,2)[2],II_,N_):\012 [[img1__[1],img1__[2]],[img2__[1],img2__[2]]]:\012 end proc:\012View_p := proc(f_,II_,N_,Mrg_) local img__:\012 img__ := Img2(f_,II_,N_):\012 if nops(Mrg_)=1 then [img__[1,1]-Mrg_[1]..img__[1,2]+Mrg_[1],img__[2,1]-Mrg_[1]..img__[2,2]+Mrg_[1]]\012  else [img__[1,1]-Mrg_[1]..img__[1,2]+Mrg_[2],img__[2,1]-Mrg_[3]..img__[2,2]+Mrg_[4]]\012  end if:\012 end proc:\012ImDom := proc(II_,phi_) local k__:\012 [seq( [min(phi_(II_[k__][1]),phi_(II_[k__][2])),max(phi_(II_[k__][1]),phi_(II_[k__][2]))] , k__=1..nops(II_) )]:\012 end proc:\012Recup := proc(str_,eps_,inf_) local str__,sgn__,x__:\012 sgn__ := StringTools[Take](StringTools[Reverse](str_),1):\012 if (sgn__=&quot;+&quot; or sgn__=&quot;-&quot;) then str__ := StringTools[Take](str_,StringTools[Length](str_)-1)\012                             else str__ := str_\012                             end if: \012 x__ := parse(str__):\012 if str__=&quot;+inf&quot;       then [+infinity,inf_]\012  else if str__=&quot;-inf&quot; then [-infinity,-inf_]\012  else if sgn__=&quot;+&quot;    then [x__,x__+eps_]\012  else if sgn__=&quot;-&quot;    then [x__,x__-eps_]\012  else                      [x__,x__]\012  end if end if end if\012 end if:\012 end proc:\012IIRecup := proc(II_,Eps_,Inf_) local k__,L1__,L2__:\012 L1__ := [ seq( Recup(II_[k__][1],Eps_[k__][1],Inf_[k__][1]) , k__=1..nops(II_) ) ]:\012 L2__ := [ seq( Recup(II_[k__][2],Eps_[k__][2],Inf_[k__][2]) , k__=1..nops(II_) ) ]:\012 [ [ seq( [L1__[k__][1],L2__[k__][1]] , k__=1..nops(II_) ) ] , [ seq( [L1__[k__][2],L2__[k__][2]] , k__=1..nops(II_) ) ] ]:\012 end proc:\012lim := proc(f_,x0_) local sgn__,x__,x0__:\012 sgn__ := StringTools[Take](StringTools[Reverse](x0_),1):\012 if (sgn__=&quot;+&quot; or sgn__=&quot;-&quot;) then x0__ := parse(StringTools[Take](x0_,StringTools[Length](x0_)-1))\012                             else x0__ := parse(x0_)\012  end if:\012 if x0_=&quot;+inf&quot;        then limit(f_(x__),x__=infinity)\012  else if x0_=&quot;-inf&quot;  then limit(f_(x__),x__=-infinity)\012   else if sgn__=&quot;+&quot;  then limit(f_(x__),x__=x0__,right)\012    else if sgn__=&quot;-&quot; then limit(f_(x__),x__=x0__,left)\012     else                   limit(f_(x__),x__=x0__)\012     end if\012    end if\012   end if\012  end if:\012 end proc:\012Approx := (n_,val_) -&gt; [seq( [val_,val_] , k__=1..n_ )]:\012\012end module:                                                                                          \012                                                                                                            \012###################################################### GEOMETRIE #################################################################\012\012Geometrie := module()                                                                                       \012\012  uses     plots, LinearAlgebra, AnimationII; \012  export   POL, SPH, M_dat, A_dat, P_dat, L_dat, E_dat, MAPLE_dat,\012           bar2, bar3, Bar2, Bar3, polyreg, BAR2_1, BAR2_2, curvecoords, polarcoords, lincartcoords, \012             linpolcoords, detplot, CharPlot, WordPlot,\012           CharParam, WordParam, curvecoords3d, sphericalcoords3d, lincartcoords3d, \012             linsphcoords3d, detplot3d;\012  local    Paragraphe;\012  option package;\012\012Paragraphe := &quot;Constantes &amp; Variables globales&quot;:                                                            \012POL := [0,2*Pi]: SPH := [[0,2*Pi],[0,Pi]]:\012M_dat := [&lt;0,0&gt;,&lt;0,1&gt;,&lt;0.5,0.5&gt;,&lt;1,1&gt;,&lt;1,0&gt;]:\012A_dat := [&lt;0,0&gt;,&lt;0.5,1&gt;,&lt;1,0&gt;,&lt;0.75,0.5&gt;,&lt;0.25,0.5&gt;]:\012P_dat := [&lt;0,0&gt;,&lt;0,1&gt;,&lt;1,1&gt;,&lt;1,0.5&gt;,&lt;0,0.5&gt;]:\012L_dat := [&lt;0,1&gt;,&lt;0,0&gt;,&lt;1,0&gt;]:\012E_dat := [&lt;1,0&gt;,&lt;0,0&gt;,&lt;0,0.5&gt;,&lt;0.5,0.5&gt;,&lt;0,0.5&gt;,&lt;0,1&gt;,&lt;1,1&gt;]:\012MAPLE_dat := [M_dat,A_dat,P_dat,L_dat,E_dat]:\012 Paragraphe := &quot;G\303\251om\303\251trie&quot;:                                                                                \012bar2     := (M_,N_,t_)          -&gt; map(expand,evalf((1-t_)*M_+t_*N_)):\012bar3     := (M_,N_,P_,s_,t_)    -&gt; map(expand,evalf((1-s_-t_)*M_+s_*N_+t_*P_)):\012Bar2     := (MM_,NN_,t_)        -&gt; [seq(bar2(MM_[k__],NN_[k__],t_),k__=1..nops(MM_))]:\012Bar3     := (MM_,NN_,PP_,s_,t_) -&gt; [seq(bar3(MM_[k__],NN_[k__],PP_[k__],s_,t_),k__=1..nops(MM_))]:\012polyreg  := (n_,N_)             -&gt;  [seq(evalf(&lt;cos(k__*2*Pi/n_),sin(k__*2*Pi/n_)&gt;),k__=0..N_-1)]:\012BAR2_1   := proc(MM_,t_) local MMMM__:\012 MMMM__ := RElist1(MM_): Bar2(MMMM__[1],MMMM__[2],t_):\012 end proc:\012BAR2_2   := proc(MM_,t_) local MMMM__:\012 MMMM__ := RElist2(MM_): Bar2(MMMM__[1],MMMM__[2],t_):\012 end proc:\012                                                                                                            \012CharParam := proc(M_,A_,a_,b_) local dil__,par__,M__:\012 dil__ := (U__,t__) -&gt; &lt;a_(t__)*U__[1],b_(t__)*U__[2]&gt;:\012 M__   := (k__,t__) -&gt; dil__(M_[k__],t__):\012 [seq( unapply(A_(t__)+(1-s__)*M__(k__,t__)+s__*M__(k__+1,t__),s__,t__), k__=1..nops(M_)-1 )]:\012 end proc:\012WordParam := proc(MM_,A_,a_,b_,space_) local dil__,MM__,a__,A__:\012 dil__ := (U__,t__) -&gt; &lt;a_(t__)*U__[1],b_(t__)*U__[2]&gt;:\012 MM__  := (l__,k__,t__) -&gt; dil__(MM_[l__][k__],t__):\012 a__   := (l__,t__) -&gt; (l__-1)*a_(t__)*(1+space_):\012 A__   := (l__,t__) -&gt; &lt;A_(t__)[1]+a__(l__,t__),A_(t__)[2]&gt;:\012 [seq( seq( unapply(A__(l__,t__)+(1-s__)*MM__(l__,k__,t__)+s__*MM__(l__,k__+1,t__),s__,t__), \012  k__=1..nops(MM_[l__])-1 ), l__=1..nops(MM_) )]:\012 end proc:\012curvecoords    := proc(F_) local G__,R__,V__,default__,coords__,t__:\012 G__  := 20,20:\012 R__ := -1..1,-1..1:\012 V__ := R__:\012 default__ := [R__,G__,V__]:\012 addcoords(coords__,[seq(t__[j__],j__=1..2)],V2L(F_(t__)),default__):\012 coords__:\012 end proc:\012polarcoords   := proc() local F__:\012 F__ := t__ -&gt; &lt;t__[1]*cos(t__[2]),t__[1]*sin(t__[2])&gt;:\012 curvecoords(F__):\012 end proc:\012lincartcoords := proc(B_) local F__:\012 F__  := t__ -&gt; [seq(CombLinS(B_,t__)[j__],j__=1..2)]:\012 curvecoords(F__):\012 end proc:\012linpolcoords  := proc(A_) local pol__,F__:\012 pol__ := t__ -&gt; &lt;t__[1]*cos(t__[2]),t__[1]*sin(t__[2])&gt;:\012 F__  := t__ -&gt; [seq(CombLinS(M2L(A_),pol__(t__))[j__],j__=1..2)]:\012 curvecoords(F__):\012 end proc:\012detplot := proc(A_,n_) local F__,g__,max__:\012 F__   := (t__,x__,y__) -&gt; (1/t__)*(A_^(-1)).&lt;x__,y__&gt;:\012 max__ := 2*Norm(A_,1)+Norm(A_.&lt;1/2,1/2&gt;,infinity):\012 g__   := t__ -&gt; implicitplot( Norm(F__(t__,x__,y__)-&lt;1/2,1/2&gt;,infinity)=1/2,\012                               x__=0..max__,y__=0..max__,gridrefine=4       ):\012 plots[display]( [seq( g__(k__/n_) , k__=1..n_ ) ] , axes=normal ):\012 end proc:\012CharPlot := proc(M_,AT_,A_,a_,b_,t_) local ff__: \012 ff__ :=  CharParam(M_,A_,a_,b_):\012 NW_CurveParam([ff__,I_01],AT_,t_):\012 end proc:\012WordPlot := proc(MM_,AT_,A_,a_,b_,space_,t_) local FF__:\012 FF__ :=  WordParam(MM_,A_,a_,b_,space_):\012 NW_CurveParam([FF__,I_01],AT_,t_):\012 end proc:\012                                                                                                            \012curvecoords3d := proc(F_) local G__,R__,V__,default__,coords__,t__:\012 G__  := [seq(k__/10,k__=0..10)]:\012 R__ := [-1..1,-1..1,-1..1]:\012 V__ := R__:\012 default__ := [G__,G__,G__,R__,V__]:\012 addcoords(coords__,[seq(t__[j__],j__=1..3)],convert(F_(t__),list),default__):\012 coords__:\012 end proc:\012sphericalcoords3d := proc() local F__:\012 F__ := t__ -&gt; \012  &lt;t__[1]*cos(t__[2])*sin(t__[3]),t__[1]*sin(t__[2])*sin(t__[3]),t__[1]*cos(t__[3])&gt;:\012 curvecoords3d(F__):\012 end proc:\012lincartcoords3d := proc(B_) local F__:\012 F__  := t__ -&gt; [seq(CombLinS(B_,t__)[j__],j__=1..3)]:\012 curvecoords3d(F__):\012 end proc:\012linsphcoords3d := proc(A_) local sph__,F__:\012 sph__ := t__ -&gt; \012  &lt;t__[1]*cos(t__[2])*sin(t__[3]),t__[1]*sin(t__[2])*sin(t__[3]),t__[1]*cos(t__[3])&gt;:\012 F__  := t__ -&gt; [seq(CombLinS(M2L(A_),sph__(t__))[j__],j__=1..3)]:\012 curvecoords3d(F__):\012 end proc:\012detplot3d := proc(A_,n_) local F__,g__,max__:\012 F__   := (t__,x__,y__,z__) -&gt; (1/t__)*(A_^(-1)).&lt;x__,y__,z__&gt;:\012 max__ := 2*Norm(A_,1)+Norm(A_.&lt;1/2,1/2,1/2&gt;,infinity):\012 g__   := t__ -&gt; implicitplot3d( Norm(F__(t__,x__,y__,z__)-&lt;1/2,1/2,1/2&gt;,infinity)=1/2,\012                                 x__=0..max__,y__=0..max__,z__=0..max__,grid=[10,10,10] ):\012 plots[display]( [seq( g__(k__/n_) , k__=1..n_ ) ] , axes=normal, style=patchnogrid ):\012 end proc:\012\012end module:                                   \012\012#################################################### PROBCOMB###################################################################\012\012ProbComb := module()                                                                                      \012\012  uses     plots, LinearAlgebra, StringTools, ListTools,\012           AnimationII, AlgLin, Analyse, Geometrie; \012  export   OPT0,\012           last, l2l1, l1l2, L2L1, L1L2, ll2t, swq, repeat, nr2v, v2nr, b2p, rot45, invrot45, \012           DisplayP, DisplayW, PrintP, PrintW, PrintF, PrintI,\012           Succ, Pred, nodeT, NodeT, nodeP, NodeP, Node, blade, biss, \012           rule_null, Range, Rule, ModifyBF, Name, \012           Prob, Vertices, Universe, Joker, Event, ProbEvent,\012           DisplayEventProb, DisplayEventSet, PrintEventProb, PrintEventSet,\012           Data1, Data2, Data3, Data, EventData1, EventData2, EventData3, EventData,\012           EmptyTree, Tree, UnivTree, EventTree, HighLight,\012           PathNode, PathData1, PathData2, PathData3, PathData, EventPathData, UnivPath, EventPath,\012           EventWalk;\012  local    paragraphe;\012option package;\012\012                                                                                                          \012                                                                                                          \012OPT0 := table([ &quot;ij&quot; = [1,8], &quot;eps&quot; = 0.1, &quot;hs&quot; = 1.5, &quot;vs&quot; = 2, &quot;br&quot; = 3, &quot;mo&quot; = &quot;T&quot; ]):\012                                                                                                          \012\012last := L_ -&gt; L_[nops(L_)]:\012l1l2 := L_ -&gt; [seq( [L_[1][k__],L_[2][k__]], k__=1..nops(L_[1])) ]:\012l2l1 := L_ -&gt; [ [seq(L_[k__][1], k__=1..nops(L_))] , [seq(L_[k__][2], k__=1..nops(L_))] ]:\012L2L1 := LL_ -&gt; [ [seq([seq(LL_[n__][r__][1],r__=1..nops(LL_[n__]))],n__=1..nops(LL_))], \012                 [seq([seq(LL_[n__][r__][2],r__=1..nops(LL_[n__]))],n__=1..nops(LL_))] ]:\012L1L2 := LL_ -&gt; [seq( [seq([LL_[1][n__][r__],LL_[2][n__][r__]],r__=1..nops(LL_[n__]))], n__=1..nops(LL_) )]:\012ll2t := (LL_,br_) -&gt; ListTools[Flatten]([seq([op(LL_[k__]),br_],k__=1..nops(LL_)-1),last(LL_)]):\012swq := s__ -&gt; parse(convert(s__,string)):\012repeat := (n_,b_) -&gt; [seq(b_,k__=1..n_)]:\012nr2v := proc(nr_,B_) local q__,v__,n__:\012 q__ := nr_[2]-1: \012 v__ := []:\012 n__ := nr_[1]:\012 while q__&lt;&gt;0 do\012  v__ := [op(v__),irem(q__,B_[n__])]: \012  q__ := iquo(q__,B_[n__]): \012  n__ := n__-1:\012  end do:\012 v__ := map(x__-&gt;x__+1,v__):\012 v__ := ListTools[Reverse](v__):\012 if nr_=[0,0] then [1] else [seq(1,k__=1..nr_[1]-nops(v__)),op(v__)] end if:\012 end proc:\012v2nr := proc(v_,B_,n_:=nops(v_)) local b__,r__,k__:\012 b__ := 1: \012 r__ := 0:\012 for k__ from n_ to 2 by -1 do\012  r__ := r__ + (v_[k__]-1)*b__:\012  b__ := b__*B_[k__]:\012  end do:\012 r__ := r__ + (v_[1]-1)*b__:\012 [n_,r__+1]:\012 end proc:\012b2p := proc(bb_) local i__,s__,p__:\012 s__ := add(bb_[i__], i__=1..nops(bb_)):\012 [seq( [bb_[i__],s__], i__=1..nops(bb_) )]:\012 end proc:\012rot45 := M_ -&gt; [(M_[1]-M_[2])/2,(M_[1]+M_[2])/2]:\012invrot45 := m_ -&gt; [m_[1]+m_[2],-m_[1]+m_[2]]:\012DisplayP := proc(p_,plab_) local p__:\012 if       plab_ = 'cb' then p__ := [p_[1]]:\012  else if plab_ = 'pr' then p__ := [p_[1],&quot;/&quot;,p_[2]]:\012  else if plab_ = 'sq' then p__ := [p_]:\012  else if plab_ = 'op' then p__ := p_:\012  else                      p__ := [p_]:\012  end if end if end if end if:\012 p__:\012 end proc:\012DisplayW := proc(v_,B_,WW_,vlab_) local k__,w__,nr__:\012 if vlab_ = 'cc' \012  then w__ := &quot;&quot;:\012       for k__ from 1 to nops(v_) do \012        nr__ := v2nr(v_,B_,k__):\012        w__ := [op(w__),WW_[nr__[1]][nr__[2]]] end do:\012  else if vlab_ = 'la' \012   then nr__ := v2nr(v_,B_):\012        w__ := [WW_[nr__[1]][nr__[2]]]:\012  else if vlab_ = 'sq' \012   then w__ := []:\012        for k__ from 1 to nops(v_) do \012        nr__ := v2nr(v_,B_,k__):\012        w__ := [op(w__),WW_[nr__[1]][nr__[2]]] end do: \012        w__ := [w__]: \012  else  if vlab_ = 'op'\012   then nr__ := v2nr(v_,B_):\012        w__ := WW_[nr__[1]][nr__[2]]:\012  else  w__ := [v_]:\012  end if end if end if end if:\012 w__:\012 end proc:\012PrintP := proc(p_,plab_) local p__:\012 if       plab_ = 'cb' then p__ := [p_[1]]:\012  else if plab_ = 'pr' then p__ := cat(p_[1],&quot;/&quot;,p_[2]):\012  else if plab_ = 'sq' then p__ := [p_]:\012  else if plab_ = 'op' then p__ := p_:\012  else                      p__ := [p_]:\012  end if end if end if end if:\012 p__:\012 end proc:\012PrintW := proc(v_,B_,WW_,vlab_) local k__,w__,nr__:\012 if vlab_ = 'cc' \012  then w__ := &quot;&quot;:\012       for k__ from 1 to nops(v_) do \012        nr__ := v2nr(v_,B_,k__):\012        w__ := cat(op(w__),WW_[nr__[1]][nr__[2]]) \012        end do:\012  else if vlab_ = 'la' \012   then nr__ := v2nr(v_,B_):\012        w__ := [swq(WW_[nr__[1]][nr__[2]])]:\012  else if vlab_ = 'sq' \012   then w__ := []:\012        for k__ from 1 to nops(v_) do \012         nr__ := v2nr(v_,B_,k__):\012         w__ := [op(w__),swq(WW_[nr__[1]][nr__[2]])] \012         end do: \012        w__ := [w__]: \012  else  if vlab_ = 'op'\012   then nr__ := v2nr(v_,B_):\012        w__ := cat(op(WW_[nr__[1]][nr__[2]])):\012  else  w__ := [v_]:\012  end if end if end if end if:\012 w__:\012 end proc:\012PrintI := x_ -&gt; InertForm[Display](InertForm[Parse](x_),inert=false):\012PrintF := proc(x_,vis_)\012 if vis_ = 'no' then &quot;&quot; else x_ end if:\012 end proc:\012Succ  := proc(nr_,B_) local n__,r__:\012 n__ := nr_[1]: r__ := nr_[2]:\012 [n__+1,[(r__-1)*B_[n__+1]+1,r__*B_[n__+1]]]:\012 end proc:\012Pred  := proc(nr_,B_) local n__,r__:\012 n__ := nr_[1]: r__ := nr_[2]:\012 if n__&gt;1 then [n__-1,floor((r__-1)/B_[n__])+1] else [0,0] end if:\012 end proc:\012nodeT := (o_,ij_,b_,l_) -&gt; [o_[1]+ij_[1],o_[2]+ij_[2]*(l_-(b_+1)/2)]:\012NodeT := proc(B_,o_,OPT_:=OPT0) local n__,k__,r__,ij__,B__,O__,OO__: \012 B__ := 1: \012 ij__ := OPT_[&quot;ij&quot;]:\012\012 OO__ := [[o_]]: \012 for n__ from 1 to nops(B_) do\012  ij__ := [ij__[1],ij__[2]/B_[n__]]:\012  O__ := []: \012  for r__ from 1 to B__ do\012   for k__ from 1 to B_[n__] do\012    O__ := [op(O__),nodeT(OO__[n__][r__],ij__,B_[n__],k__)]\012    end do \012   end do:\012  B__ := B__*B_[n__]: \012  OO__ := [op(OO__),O__]:\012  end do:\012\012 OO__:\012 end proc:\012nodeP := (o_,ij_,b_,l_) -&gt; [o_[1]+ij_[1],o_[2]+ij_[2]*(-1)^l_]:\012NodeP := proc(B_,o_,OPT_:=OPT0) local n__,k__,r__,ij__,B__,O__,OO__:\012 ij__ := OPT_[&quot;ij&quot;]:\012 B__ := 1: \012 \012 OO__ := [[o_]]: \012 for n__ from 1 to nops(B_) do\012  O__ := []: \012  for r__ from 1 to B__ do\012   for k__ from 1 to B_[n__] do\012    O__ := [op(O__),nodeP(OO__[n__][r__],ij__,B_[n__],k__)]\012    end do \012   end do:\012  B__ := B__*B_[n__]: \012  OO__ := [op(OO__),O__]:\012  end do:\012\012 OO__:\012 end proc:\012Node :=  proc(B_,o_,OPT_:=OPT0) local mode__:\012 mode__ := OPT_[&quot;mo&quot;]:\012 if       mode__ = &quot;T&quot; then NodeT(B_,o_,OPT_) \012  else if mode__ = &quot;P&quot; then NodeP(B_,o_,OPT_)\012  end if end if:\012 end proc:\012blade := proc(o1_,o2_,t_,p_,w_,e_,at_,JOK_,OPT_:=OPT0) local w__,t__,o__,p__, col__, sty__,fss__, \012                                                             pt__i, pt__a, pt__g, dk__i, dk__a,dk__g,\012                                                             aw__i,aw__a,aw__g, tx__i,tx__a,tx__g:\012 col__ := at_[1]: sty__ := at_[2]: fss__ := at_[3]:\012 if evalb(w_ in JOK_) then sty__ := ['dot',sty__[2],sty__[3]]:\012                           w__ := &quot;&quot;:\012                      else w__ := w_:\012                      end if:\012 o__   := (1-t_)*o1_+t_*o2_:\012 pt__i := o2_:\012 pt__a := [col__[1],w__,sty__[3],fss__[1]]: \012 pt__g := nw_text(pt__i,pt__a):\012 aw__a := [col__[2],'nul',sty__[1],sty__[2]]:\012 aw__i := [o1_,o2_]:\012 aw__g := nw_line(aw__i,aw__a):\012 tx__i := [o__[1],o__[2]+e_]:\012 tx__a := [col__[3],p_,'nul',fss__[2]]:\012 tx__g := nw_text(tx__i,tx__a):\012\012 display([pt__g,aw__g,tx__g], axes=none, scaling=constrained):\012 end proc:\012biss := proc(n_,o_,at_,OPT_) local ij__,col__,sty__,biss__i,biss__a,biss__g:\012 ij__ := OPT_[&quot;ij&quot;]:\012 col__ := at_[1]: sty__ := at_[2]:\012 biss__i := [o_,[o_[1]+(n_+1)*ij__[1],o_[2]]]:\012 biss__a := [col__[2],'nul',sty__[1],sty__[2]]:\012 biss__g := nw_line(biss__i,biss__a):\012 display(biss__g):\012 end proc:\012                                                                                                          \012rule_null := (BF_,n_,bb_,i_) -&gt; [seq( 0,k__=1..nops(BF_[n_](bb_,i_)) )]:\012Range := proc(XF_) local bb__,n__,B__:\012 bb__ := XF_[1]:\012 B__ := [nops(bb__)]:\012 for n__ from 2 to nops(XF_) do \012  bb__ := XF_[n__](bb__,1):\012  B__ := [op(B__),nops(bb__)]:\012  end do:\012 B__:\012 end proc:\012Rule := proc(BF_,X_:=NULL) local n__,r__,i__,b__,bb__,BB__,Bb__:\012 bb__ := BF_[1]:\012 BB__ := [[bb__]]: \012 for n__ from 1 to nops(BF_)-1 do\012  Bb__ := []: \012  for r__ from 1 to nops(BB__[n__]) do\012   bb__ := BB__[n__][r__]:\012   for i__ from 1 to nops(bb__) do\012    if bb__[i__]=0 then b__ := rule_null(BF_,n__,bb__,i__)\012                   else b__ := BF_[n__+1](bb__,i__,X_)\012                   end if:\012    Bb__ := [op(Bb__),b__]:\012    end do end do:\012  BB__ := [op(BB__),Bb__]:\012  end do:\012\012 BB__:\012 end proc:\012ModifyBF := proc(var_,max_,BF1_,BF2_) local n__,k__,BF__:\012 n__ := nops(var_):\012 BF__ := BF1_:\012 for k__ from 1 to n__ do\012  if var_[k__]&lt;=max_[k__] then BF__[k__] := BF2_[k__] end if:\012  end do:\012 BF__:\012 end proc:\012                                                                                                          \012Name := proc(WF_,X_:=NULL) local n__,r__,i__,w__,ww__,WW__,Ww__:\012 ww__ := WF_[1]:\012 WW__ := [[ww__]]: \012 for n__ from 1 to nops(WF_)-1 do\012  Ww__ := []: \012  for r__ from 1 to nops(WW__[n__]) do\012   ww__ := WW__[n__][r__]:\012   for i__ from 1 to nops(ww__) do\012    w__ := WF_[n__+1](ww__,i__,X_):\012    Ww__ := [op(Ww__),w__]:\012    end do end do:\012  WW__ := [op(WW__),Ww__]:\012  end do:\012\012 [seq( [seq(op(WW__[n__][k__]),k__=1..nops(WW__[n__]))], n__=1..nops(WW__))]:\012 end proc:\012                                                                                                          \012                                                                                                          \012Prob := proc(BB_) local n__,r__,bb__,P__,PP__:\012 PP__ := []: \012 for n__ from 1 to nops(BB_) do\012  P__ := []:\012  for r__ from 1 to nops(BB_[n__]) do\012   bb__ := BB_[n__][r__]:\012   P__ := [op(P__),op(b2p(bb__))]:\012   end do:\012  PP__ := [op(PP__),P__]:\012  end do:\012\012 PP__:\012 end proc:\012Universe := proc(B_,PP_) local n__,r__,p__,v__,k__,l__,m__,nr__,vp__,VP__,VPk__,UU__:\012 n__ := nops(PP_): \012\012 VP__ := [seq([],k__=1..n__)]:\012 for r__ from 1 to nops(PP_[n__]) do\012  nr__ := [n__,r__]: \012  p__ := [1,1]: \012  while (nr__[1]&gt;=1 and PP_[nr__[1]][nr__[2]][1]=0) do \012   nr__ := Pred(nr__,B_):\012   end do:\012  v__ := nr2v(nr__,B_):\012  while nr__[1]&gt;=1 do \012   p__ := [p__[1]*PP_[nr__[1]][nr__[2]][1],p__[2]*PP_[nr__[1]][nr__[2]][2]]:\012   nr__ := Pred(nr__,B_):\012   end do:\012  VP__[nops(v__)] := [op(VP__[nops(v__)]),[v__,p__]]:\012  end do:\012 VP__ := [seq( ListTools[MakeUnique](VP__[k__]), k__=1..nops(VP__) )]:\012\012 UU__ := []:\012 for k__ from 1 to nops(VP__)-1 do\012  for vp__ in VP__[k__] do\012   m__ := 1:\012   VPk__ := VP__[k__+1]:\012   while (m__&lt;=nops(VPk__) and vp__[1]&lt;&gt;VPk__[m__][1][1..k__]) do m__ := m__+1 end do:\012   if m__&gt;nops(VPk__) then UU__ := [op(UU__),vp__] end if:\012   end do:\012  end do:\012 UU__ := [op(UU__),op(last(VP__))]:\012\012 UU__:\012 end proc:\012Joker := proc(B_,UU_,WW_,JOK_,OPT_:=OPT0) local n__,k__,m__,v__,p__,vp__,nr__,UUN__,UUJ__,\012                                                vv__,JJ__,JJN__,JJJ__,JJJ1__,JJJ2__,JJJJ__:\012 UUN__ := []: UUJ__ := []:\012 for k__ from 1 to nops(UU_) do\012  vp__ := UU_[k__]: v__ := vp__[1]: p__ := vp__[2]:\012  m__ := 1: \012  nr__ := v2nr(v__,B_,m__):\012  while evalb(m__&lt;=nops(v__) and not(WW_[nr__[1]][nr__[2]] in JOK_)) do \012   m__ := m__+1:\012   if m__&lt;=nops(v__) then nr__ := v2nr(v__,B_,m__) end if:\012   end do:\012  if m__&lt;=nops(v__) \012   then v__ := [seq(v__[k__],k__=1..m__-1),v__[m__]]:\012        UUJ__ := [op(UUJ__),[v__,p__]]:\012   else UUN__ := [op(UUN__),vp__]\012   end if:\012  end do:\012 JJ__ := [UUN__,UUJ__]:\012\012 JJN__ := JJ__[1]: JJJ__ := l2l1(JJ__[2]):  \012 JJJ1__ := JJJ__[1]: JJJ2__ := JJJ__[2]: JJJJ__ := []:\012 while nops(JJJ1__)&gt;0 do\012  v__ := JJJ1__[1]:\012  vv__ := ListTools[Reverse]([ListTools[SearchAll](v__,JJJ1__)]):\012  p__ := add(JJJ2__[k__],k__ in vv__):\012  JJJJ__ := [op(JJJJ__),[v__,p__]]:\012  for k__ from 1 to nops(vv__) do \012   JJJ1__ := subsop(vv__[k__]=NULL,JJJ1__):\012   JJJ2__ := subsop(vv__[k__]=NULL,JJJ2__):\012   end do:\012  end do:\012\012 [op(JJN__),op(JJJJ__)]:\012 end proc:\012Vertices := proc(JJ_) local n__,v__,k__,V__,VV__:\012 V__ := l2l1(JJ_)[1]: \012 n__ := max(seq(nops(V__[k__]),k__=1..nops(V__))):\012\012 VV__ := [seq([],k__=1..n__)]:\012 for v__ in V__ do \012  VV__[nops(v__)] := [op(VV__[nops(v__)]),v__]:\012  end do:\012 for k__ from 1 to nops(VV__) do\012  VV__[k__] := [op(VV__[k__]),seq( v__[1..k__],v__ in last(VV__) )]:\012  end do:\012\012 [seq( ListTools[MakeUnique](VV__[k__]), k__ = 1..nops(VV__) )]:\012 end proc:\012Event := proc(B_,UU_,EVENTRULE_,eventrule_,BB_,WW_,log_:=&quot;&quot;) local k__,v__,p__,boo__,EP__:\012 EP__ := []:\012 for k__ from 1 to nops(UU_) do\012  v__ := UU_[k__][1]: p__ := UU_[k__][2]:\012  if log_ = &quot;&quot; then boo__ := eventrule_(v__,EVENTRULE_,B_,BB_,WW_)\012               else boo__ := eventrule_(v__,EVENTRULE_,B_,BB_,WW_,log_) \012               end if:\012  if boo__ then EP__ := [op(EP__),[v__,p__]] end if:\012  end do:\012 EP__:\012 end proc:\012DisplayEventProb := proc(EE_,plab_) \012 [seq( DisplayP(e__[2],plab_), e__ in EE_ )]:\012 end proc:\012DisplayEventSet := proc(B_,EE_,WW_,vlab_) \012 [seq( DisplayW(e__[1],B_,WW_,vlab_), e__ in EE_ )]:\012 end proc:\012PrintEventProb := proc(EE_,plab_) \012 [seq( PrintP(e__[2],plab_), e__ in EE_ )]:\012 end proc:\012PrintEventSet := proc(B_,EE_,WW_,vlab_) \012 [seq( PrintW(e__[1],B_,WW_,vlab_), e__ in EE_ )]:\012 end proc:\012ProbEvent := proc(EE_,plab_) local e__,p__,p___:\012 p__ := 0:\012 for e__ in EE_ do\012  p___ := e__[2]:\012  if       plab_ = 'cb' then p__ := p__ + p___[1]\012   else if plab_ = 'pr' then p__ := p__ + p___[1]/p___[2]\012   else                       p__ := p__\012   end if end if:\012  end do:\012 p__:\012 end proc:\012                                                                                                          \012Data1 := proc(B_,JJ_,PP_,OO_,WW_,prt_,OPT_:=OPT0) local b__,o__,v__,n__,r1__,r2__,r20__,o1__,o2__,t__,w__,p__,e__,\012                                                        ij__,eps__,ww__,nr1__,nr2__,OO__,DT__,VV__,PP__:\012 eps__ := OPT_[&quot;eps&quot;]:\012\012 VV__ := Vertices(JJ_): \012 o__  := OO_[1][1]: OO__ := OO_[2..nops(OO_)]: \012\012 DT__ := [seq([],k__=1..nops(VV__))]:\012 if nops(VV__)&gt;0 then\012  b__ := B_[1]:\012  for v__ in VV__[1] do\012   nr2__ := v2nr(v__,B_,1):\012   r2__  := nr2__[2]:\012   o1__  := o__:\012   o2__  := OO__[1][r2__]:\012   t__   := 1/2:\012   w__   := WW_[nr2__[1]][nr2__[2]]: w__ := DisplayW(v__,B_,WW_,prt_[2]):\012   p__   := PP_[1][r2__]: p__ := DisplayP(p__,prt_[1]):\012   e__   := signum(r2__-1-(b__-1)/2)*eps__:\012   DT__[1] := [op(DT__[1]),[o1__,o2__,t__,p__,w__,e__]]:\012   end do:\012  end if:\012\012 for n__ from 2 to nops(VV__) do\012  b__ := b__*B_[n__]:\012  for v__ in VV__[n__] do\012   nr1__ := v2nr(v__,B_,n__-1):\012   nr2__ := v2nr(v__,B_,n__):\012   r1__  := nr1__[2]:\012   r2__  := nr2__[2]:\012   o1__  := OO__[n__-1][r1__]:\012   o2__  := OO__[n__][r2__]:\012   t__   := 1/2:\012   w__   := WW_[nr2__[1]][nr2__[2]]: w__ := DisplayW(v__,B_,WW_,prt_[2]):\012   p__   := PP_[n__][r2__]: p__ := DisplayP(p__,prt_[1]):\012   r20__ := Succ([n__-1,r1__],B_)[2][1]:\012   e__   := signum(r2__-r20__-(B_[n__]-1)/2)*eps__/b__:\012   DT__[n__] := [op(DT__[n__]),[o1__,o2__,t__,p__,w__,e__]]:\012   end do \012  end do:\012\012 [seq( op(DT__[k__]), k__ = 1..nops(DT__) )]:\012 end proc:\012Data2 := proc(B_,JJ_,OO_,WW_,pw_,prt_,OPT_:=OPT0) local k__,n__,nr__,o1__,o2__,t__,w__,p__,e__,vp__,pw__,\012                                                        ij__,hs__,OO__,P__,W__,DT__:\012 ij__ := OPT_[&quot;ij&quot;]: hs__ := OPT_[&quot;hs&quot;]:\012 \012 pw__ := l2l1(JJ_):\012 P__ := pw_[1]:  W__ := pw_[2]:\012 if P__ = [] then P__ := DisplayEventProb(JJ_,prt_[1]) end if:\012 if W__ = [] then W__ := DisplayEventSet(B_,JJ_,WW_,prt_[2]) end if:\012 \012 OO__ := OO_[2..nops(OO_)]: n__ := nops(OO__):\012\012 DT__ := []:\012 for k__ from 1 to nops(JJ_) do\012  vp__ := JJ_[k__]:\012  nr__ := v2nr(vp__[1],B_):\012  o1__ := OO__[nr__[1]][nr__[2]]:\012  o2__ := [o1__[1]+(n__-nr__[1])*ij__[1]+hs__*ij__[1],o1__[2]]:\012  t__  := 1-hs__/(2*(n__-nr__[1]+hs__)):\012  w__  := W__[k__]:\012  p__  := P__[k__]:\012  e__  := 0:\012  DT__ := [op(DT__),[o1__,o2__,t__,p__,w__,e__]]:\012  end do:\012 \012 DT__:\012 end proc:\012Data3 := proc(B_,OO_,pw_,prt_,OPT_:=OPT0) local k__,n__,y__,o__,o1__,o2__,t__,w__,p__,e__,\012                                               ij__,hs__,vs__,B__,P__,W__,OO__,DT__:\012 ij__ := OPT_[&quot;ij&quot;]: hs__ := OPT_[&quot;hs&quot;]: vs__ := OPT_[&quot;vs&quot;]: \012 n__ := nops(B_): B__ := mul(B_[k__],k__=1..n__):\012\012 P__ := pw_[1]: W__ := pw_[2]:\012 if evalb(P__ =  [] and W__ &lt;&gt; []) then P__ := [seq(&quot;&quot;,k__=1..nops(B_)+1)] end if:\012 if evalb(P__ &lt;&gt; [] and W__ =  []) then W__ := [seq(&quot;&quot;,k__=1..nops(B_)+1)] end if:\012 if evalb(P__ =  [] and W__ =  []) then n__ := 0 end if:\012\012 o__ := OO_[1][1]:\012 y__ := o__[2]-(ij__[2]/B__)*((B__+1)/2+vs__):\012 \012 DT__ := []:\012 for k__ from 1 to n__ do\012  o1__ := [o__[1]+(k__-1)*ij__[1],y__]:\012  o2__ := [o__[1]+(k__)*ij__[1],y__]:\012  t__  := 1/2:\012  w__  := W__[k__]:\012  p__  := P__[k__]:\012  e__  := 0:\012  DT__ := [op(DT__),[o1__,o2__,t__,p__,w__,e__]]:\012  end do:\012\012 if n__&gt;0 then\012  o1__ := [o__[1]+n__*ij__[1],y__]:\012  o2__ := [o1__[1]+hs__*ij__[1],y__]:\012  t__  := 1/2:\012  w__  := W__[n__+1]:\012  p__  := P__[n__+1]:\012  e__  := 0:\012  DT__ := [op(DT__),[o1__,o2__,t__,p__,w__,e__]]:\012  end if:\012\012 DT__:\012 end proc:\012Data := proc(B_,JJ_,PP_,OO_,WW_,PW_,PRT_,Chx_,OPT_:=OPT0)\012 if       Chx_[1]=1 then Data1(B_,JJ_,PP_,OO_,WW_,              PRT_[op(Chx_)],OPT_)\012  else if Chx_[1]=2 then Data2(B_,JJ_    ,OO_,WW_,PW_[op(Chx_)],PRT_[op(Chx_)],OPT_)\012  else if Chx_[1]=3 then Data3(B_        ,OO_    ,PW_[op(Chx_)],PRT_[op(Chx_)],OPT_)\012  end if end if end if:\012 end proc:\012EventData := proc(B_,JU_,JE_,PP_,OO_,WW_,PW_,PRT_,chx_,OPT_:=OPT0) local dt__,NOD__,DTU__,DTE__:\012 DTU__ := Data(B_,JU_,PP_,OO_,WW_,PW_,PRT_,[chx_,1],OPT_):\012 NOD__ := [seq(dt__[1..2],dt__ in DTU__)]:\012 DTE__ := Data(B_,JE_,PP_,OO_,WW_,PW_,PRT_,[chx_,2],OPT_):\012 for dt__ in DTE__ do\012  if member(dt__[1..2],NOD__,'k__') then \012   DTU__ := subsop(k__=NULL,DTU__):\012   NOD__ := subsop(k__=NULL,NOD__): \012   end if:\012  end do:\012 [DTU__,DTE__]:\012 end proc:\012                                                                                                          \012EmptyTree := proc() \012 display(nw_point([0,0],[&quot;White&quot;,nul,nul,point]),axes=none):\012 end proc:\012Tree := proc(DT_,prt_,at_,JOK_,OPT_:=OPT0) local s__,dt__,A__:\012 A__ := []:\012 for s__ from 1 to nops(DT_) do\012  dt__ := DT_[s__]:\012  A__ := [op(A__),blade(dt__[1],dt__[2],dt__[3],PrintF(dt__[4],prt_[1]),PrintF(dt__[5],prt_[2]),dt__[6],at_,JOK_,OPT_)]:\012  end do:\012 if DT_ = [] then EmptyTree() else display(A__) end if:\012 end proc:\012UnivTree := proc(B_,JU_,PP_,OO_,WW_,PW_,PRT_,CHX_,AT_,JOK_,OPT_:=OPT0) local k__,chx__,T__,DT__:\012 T__ := []:\012 for k__ from 1 to nops(CHX_) do\012  chx__ := CHX_[k__]:\012  DT__  := Data(B_,JU_,PP_,OO_,WW_,PW_,PRT_,[chx__,1],OPT_):\012  T__  := [op(T__),Tree(DT__,PRT_[chx__,1],AT_[chx__,1],JOK_,OPT_)]:\012  end do:\012 display(T__):\012 end proc:\012EventTree := proc(B_,JU_,JE_,PP_,OO_,WW_,PW_,PRT_,CHX_,AT_,JOK_,OPT_:=OPT0) local k__,chx__,DT__,T__:\012 T__ := []:\012 for k__ from 1 to nops(CHX_) do\012  chx__ := CHX_[k__]:\012  DT__  := EventData(B_,JU_,JE_,PP_,OO_,WW_,PW_,PRT_,chx__,OPT_):\012  T__  := [op(T__),seq(Tree(DT__[l__],PRT_[chx__,l__],AT_[chx__,l__],JOK_,OPT_),l__=1..2)]:\012  end do:\012 display(T__):\012 end proc:\012HighLight := proc(G_,V_,B_,o_,hl_,OPT_:=OPT0) local ij__,hs__,eps__,col__,sty__,tck__,n__,nr__,r__,\012                                                    v__,o__,k__,leaf__,leaf__i,leaf__a,leaf__g,OO__: \012 ij__ := OPT_[&quot;ij&quot;]: hs__ := OPT_[&quot;hs&quot;]: eps__ := OPT_[&quot;eps&quot;]:\012 col__ := hl_[1]: sty__ := hl_[2]: tck__ := hl_[3]:\012\012 OO__ := Node(B_,o_,OPT_):\012 OO__ := OO__[2..nops(OO__)]:\012\012 leaf__i := []:\012 for v__ in V_ do\012  leaf__ := [o_,o_]:\012  for n__ from 1 to nops(v__) do\012   nr__ := v2nr(v__,B_,n__):\012   r__  := nr__[2]:\012   o__  := OO__[n__][r__]:\012   leaf__ := [op(leaf__),o__]:\012   end do:\012  leaf__i := [op(leaf__i),leaf__]:\012  end do:\012 leaf__a := [col__,'nul',sty__,tck__]:\012 leaf__g := [seq([ seq( nw_line([leaf__i[k__][l__],leaf__i[k__][l__+1]],leaf__a),l__=1..nops(leaf__i[k__])-1) ],k__=1..nops(leaf__i))];\012 leaf__g := [seq(seq( display([G_,display(leaf__g[k__][1..l__])]),l__=1..nops(leaf__g[k__])),k__=1..nops(leaf__g))];\012\012 display(leaf__g,insequence=true):\012 end proc:\012                                                                                                          \012PathNode := proc(OO_) local n__,k__,o__,oo__,ooo__,O__,OO__:\012 OO__ := []:\012 for n__ from 1 to nops(OO_) do\012  O__ := OO_[n__]:\012  oo__ := ListTools[MakeUnique](O__):\012  OO__ := [op(OO__),oo__]:\012  end do:\012 OO__:\012 end proc:\012PathData1 := proc(B_,JJ_,PP_,OO_,WW_,prt_,OPT_:=OPT0) local C,k__,p__,q__,n__,pq__,DT__,OO__,WW__:\012 C := 'C':\012 DT__ := Data1(B_,JJ_,PP_,OO_,WW_,prt_,OPT_):\012 DT__ := ListTools[MakeUnique](DT__):\012 for k__ from 1 to nops(DT__) do\012  pq__ := rot45(DT__[k__][2]):\012  p__ := pq__[1]: q__ := pq__[2]: n__ := p__+q__:\012  DT__[k__][5] := [C[n__]^p__]:\012  end do:\012 DT__:\012 end proc:\012PathData2 := proc(B_,JJ_,OO_,WW_,pw_,prt_,OPT_:=OPT0) local DT__:\012 DT__ := Data2(B_,JJ_,OO_,WW_,pw_,prt_,OPT_):\012 ListTools[MakeUnique](DT__):\012 end proc:\012PathData3 := proc(B_,OO_,pw_,prt_,Chx_,OPT_:=OPT0) local k__,n__,y__,o__,o1__,o2__,t__,w__,p__,e__,\012                                                         ij__,eps__,hs__,vs__,B__,P__,W__,OO__,DT__:\012 ij__ := OPT_[&quot;ij&quot;]: eps__ := OPT_[&quot;eps&quot;]: hs__ := OPT_[&quot;hs&quot;]: vs__ := OPT_[&quot;vs&quot;]: \012 n__ := nops(B_):\012 \012 P__ := pw_[1]: W__ := pw_[2]:\012 if evalb(P__ =  [] and W__ &lt;&gt; []) then P__ := [seq(&quot;&quot;,k__=1..n__+1)] end if:\012 if evalb(P__ &lt;&gt; [] and W__ =  []) then W__ := [seq(&quot;&quot;,k__=1..n__+1)] end if:\012 if evalb(P__ =  [] and W__ =  []) then n__ := 0 end if:\012\012 OO__ := PathNode(OO_): OO__ := OO_[2..nops(OO_)]:\012 o__ := last(OO__)[1]: o__ := [o__[1]-n__*ij__[1],o__[2]-vs__]:\012 y__ := o__[2]:\012 \012 DT__ := []:\012 for k__ from 1 to n__ do\012  o1__ := [o__[1]+(k__-1)*ij__[1],y__]:\012  o2__ := [o__[1]+(k__)*ij__[1],y__]:\012  t__  := 1/2:\012  w__  := W__[k__]:\012  p__  := P__[k__]:\012  e__  := 0:\012  DT__ := [op(DT__),[o1__,o2__,t__,p__,w__,e__]]:\012  end do:\012\012 if n__&gt;0 then\012  o1__ := [o__[1]+n__*ij__[1],y__]:\012  o2__ := [o1__[1]+hs__*ij__[1],y__]:\012  t__  := 1/2:\012  w__  := W__[n__+1]:\012  p__  := P__[n__+1]:\012  e__  := 0:\012  DT__ := [op(DT__),[o1__,o2__,t__,p__,w__,e__]]:\012  end if:\012\012 if Chx_[2]=1 then \012  for k__ from 1 to n__ do\012   o1__ := OO__[k__][1]:\012   o2__ := [o1__[1],y__-eps__]:\012   t__  := 1:\012   w__  := cat(&quot;p+q=&quot;,k__):\012   p__  := &quot;&quot;:\012   e__  := -eps__:\012   DT__ := [op(DT__),[o1__,o2__,t__,p__,w__,e__]]:\012   end do:\012  end if:\012\012 DT__:\012 end proc:\012PathData := proc(B_,JJ_,PP_,OO_,WW_,PW_,PRT_,Chx_,OPT_:=OPT0)\012 if       Chx_[1]=1 then PathData1(B_,JJ_,PP_,OO_,WW_              ,PRT_[op(Chx_)]     ,OPT_)\012  else if Chx_[1]=2 then PathData2(B_,JJ_    ,OO_,WW_,PW_[op(Chx_)],PRT_[op(Chx_)]     ,OPT_)\012  else if Chx_[1]=3 then PathData3(B_        ,OO_    ,PW_[op(Chx_)],PRT_[op(Chx_)],Chx_,OPT_)\012  end if end if end if:\012 end proc:\012EventPathData := proc(B_,JU_,JE_,PP_,OO_,WW_,PW_,PRT_,chx_,OPT_:=OPT0) local pdt__,PNOD__,PDTU__,PDTE__:\012 PDTU__ := PathData(B_,JU_,PP_,OO_,WW_,PW_,PRT_,[chx_,1],OPT_):\012 PNOD__ := [seq(pdt__[1..2],pdt__ in PDTU__)]:\012 PDTE__ := PathData(B_,JE_,PP_,OO_,WW_,PW_,PRT_,[chx_,2],OPT_):\012 for pdt__ in PDTE__ do\012  if member(pdt__[1..2],PNOD__,'k__') then \012   PDTU__ := subsop(k__=NULL,PDTU__):\012   PNOD__ := subsop(k__=NULL,PNOD__): \012   end if:\012  end do:\012 [PDTU__,PDTE__]:\012 end proc:\012UnivPath := proc(B_,JU_,PP_,OO_,WW_,PW_,PRT_,CHX_,AT_,JOK_,OPT_:=OPT0) local k__,chx__,T__,PDT__:\012 T__ := [biss(nops(OO_)-1,OO_[1][1],AT_[1,1],OPT_)]:\012 for k__ from 1 to nops(CHX_) do\012  chx__ := CHX_[k__]:\012  PDT__  := PathData(B_,JU_,PP_,OO_,WW_,PW_,PRT_,[chx__,1],OPT_):\012  T__  := [op(T__),Tree(PDT__,PRT_[chx__,1],AT_[chx__,1],JOK_,OPT_)]:\012  end do:\012\012 display(T__):\012 end proc:\012EventPath := proc(B_,JU_,JE_,PP_,OO_,WW_,PW_,PRT_,CHX_,AT_,JOK_,OPT_:=OPT0) local k__,chx__,PDT__,T__:\012 T__ := [biss(nops(OO_)-1,OO_[1][1],AT_[1,1],OPT_)]:\012 for k__ from 1 to nops(CHX_) do\012  chx__ := CHX_[k__]:\012  PDT__  := EventPathData(B_,JU_,JE_,PP_,OO_,WW_,PW_,PRT_,chx__,OPT_):\012  T__  := [op(T__),seq(Tree(PDT__[l__],PRT_[chx__,l__],AT_[chx__,l__],JOK_,OPT_),l__=1..2)]:\012  end do:\012 display(T__):\012 end proc:\012EventWalk := proc(G_,v_,B_,o_,hl_,OPT_:=OPT0) local ij__,hs__,eps__,col__,sty__,tck__,\012                                                    OO__,n__,nr__,r__,o__,x__,y__,k__,\012                                                    leaf__i,leaf__a,leaf__g,walk__i,walk__a,walk__g,\012                                                    walk__leaf: \012 ij__ := OPT_[&quot;ij&quot;]: hs__ := OPT_[&quot;hs&quot;]: eps__ := OPT_[&quot;eps&quot;]:\012 col__ := hl_[1]: sty__ := hl_[2]: tck__ := hl_[3]:\012\012 OO__ := Node(B_,o_,OPT_):\012 OO__ := OO__[2..nops(OO__)]:\012 leaf__i := [o_,o_]:\012 x__ := o_[1]+(nops(B_)+hs__)*ij__[1]:\012 y__ := o_[2]: \012 walk__i := [[x__,y__],[x__,y__]]:\012 \012 n__ := 1:\012 nr__ := v2nr(v_,B_,n__):\012 r__  := nr__[2]:\012 o__  := OO__[n__][r__]:\012 leaf__i := [op(leaf__i),o__]:\012 if v_[n__] = 1 then y__ := y__ - ij__[2] else y__ := y__ + ij__[2] end if:\012 walk__i := [op(walk__i),[x__,y__]]:\012 \012 for n__ from 2 to nops(v_) do\012  nr__ := v2nr(v_,B_,n__):\012  r__  := nr__[2]:\012  o__  := OO__[n__][r__]:\012  if v_[n__-1] &lt;&gt; v_[n__] then x__ := x__+ eps__: \012                               walk__i := [op(walk__i),[x__,y__]]: \012                               leaf__i := [op(leaf__i),last(leaf__i)]:\012   end if:\012  if v_[n__] = 1 then y__ := y__ - ij__[2] else y__ := y__ + ij__[2] end if:\012  leaf__i := [op(leaf__i),o__]:\012  walk__i := [op(walk__i),[x__,y__]]:\012  end do:\012\012 leaf__a := [col__,'nul',sty__,tck__]:\012 leaf__g := [seq(nw_line([leaf__i[k__],leaf__i[k__+1]],leaf__a),k__=1..nops(leaf__i)-1)]:\012 leaf__g := [seq(display([G_,op(leaf__g[1..k])]),k=1..nops(leaf__g))]:\012 walk__a := [col__,'nul',sty__,tck__]:\012 walk__g := [seq(nw_line([walk__i[k__],walk__i[k__+1]],walk__a),k__=1..nops(walk__i)-1)]:\012 walk__g := [seq(display([G_,op(walk__g[1..k])]),k=1..nops(walk__g))]:\012\012 walk__leaf := [seq(display([walk__g[k__],leaf__g[k__]]),k__=1..nops(walk__g))]:\012 \012 display(walk__leaf,scaling=constrained,insequence=true):\012 end proc:\012end module:                                                                                                                                                          \012\012#################################################### PROBMISC###################################################################\012\012ProbMisc := module()                                                                                      \012\012  uses     plots, LinearAlgebra, StringTools, ListTools,\012           AnimationII, AlgLin, Analyse, Geometrie, ProbComb; \012  export   PW0, PW1,\012           PRTnn, PRTnc, PRTnl, PRTns, PRTni, PRTno, PRTcn, PRTcc, PRTcl, PRTcs, PRTci, PRTco, \012           PRTpn, PRTpc, PRTpl, PRTps, PRTpi, PRTpo, PRTsn, PRTsc, PRTsl, PRTss, PRTsi, PRTso,\012           PRTin, PRTic, PRTil, PRTis, PRTii, PRTio, PRTon, PRToc, PRTol, PRTos, PRToi, PRToo,\012           PseudoString2List, PseudoList2List, RealList2List, RealList2String, FixedPoint, DeleteByRank, \012           TypeList,\012           rule_nssr, rule_nsar, rule_tasr, rule_taar, rule_dec,\012           name_comb_l, name_perm_l, name_multiperm_l, name_dec,\012           event_empty, event_full, event_all, event_sample, \012           event_isin_nset_wset, event_isin_nseq_wseq, event_iseq_wone_nany, \012           event_isin_wone_nany, event_isin_wset_alone, event_isin_ww_anywhere,\012           event_less_wone_numb, event_equal_wone_numb, event_more_wone_numb, \012           event_path_through_each, event_path_side_which, event_path_side_end,\012           event_fix_equal_set, event_fix_include_set, event_fix_equal_nb, event_fix_more_nb,\012           event_strict_increase, event_isin_wset;\012  local    paragraphe;\012option package;\012\012                                                                                                          \012                                                                                                          \012                                                                                                          \012PRTnn := ['no','no']: PRTnc := ['no','cc']: PRTnl := ['no','la']: PRTns := ['no','sq']: PRTni := ['no','id']: PRTno := ['no','op']:\012PRTcn := ['cb','no']: PRTcc := ['cb','cc']: PRTcl := ['cb','la']: PRTcs := ['cb','sq']: PRTci := ['cb','id']: PRTco := ['cb','op']:\012PRTpn := ['pr','no']: PRTpc := ['pr','cc']: PRTpl := ['pr','la']: PRTps := ['pr','sq']: PRTpi := ['pr','id']: PRTpo := ['pr','op']:\012PRTsn := ['sq','no']: PRTsc := ['sq','cc']: PRTsl := ['sq','la']: PRTss := ['sq','sq']: PRTsi := ['sq','id']: PRTso := ['sq','op']:\012PRTin := ['id','no']: PRTic := ['id','cc']: PRTil := ['id','la']: PRTis := ['id','sq']: PRTii := ['id','id']: PRTio := ['id','op']:\012PRTon := ['op','no']: PRToc := ['op','cc']: PRTol := ['op','la']: PRTos := ['op','sq']: PRToi := ['op','id']: PRToo := ['op','op']:\012PW0 := [[],[]]: PW1 := m -&gt; [[seq(1,k=1..m)],[seq(&quot;&quot;,k=1..m)]]:\012                                                                                                          \012PseudoString2List := proc(s_) local n__,k__,s__,l__,m__:\012 n__ := StringTools[Length](s_):\012 k__ := 1:\012 s__ := [convert(s_[1],name)]:\012 while k__ &lt; n__ do\012  l__ := k__+1: \012  if StringTools[IsDigit](s_[l__]) \012   then while evalb( l__ &lt; n__ and StringTools[IsDigit](s_[l__])) do l__ := l__+1: end do:\012         if `not`(StringTools[IsDigit](s_[l__])) then l__ := l__-1 end if:\012         m__ := parse(s_[k__+1..l__]):\012         s__ := [op(s__[1..nops(s__)-1]),s__[nops(s__)][m__]]:\012   else s__ := [op(s__),convert(s_[l__],name)]:\012   end if: \012  k__ := l__:\012  end do:\012 if k__ &lt; n__ then s__ := [op(s__),s_[n__]] end if:\012 s__ :\012 end proc:\012PseudoList2List := proc(L_) local s__:\012 s__ := map(convert,L_,string):\012 map(op,map(PseudoString2List,s__)):\012 end proc:\012RealList2List := proc(L_) local k__,s__,L__:\012 L__ := []:\012 for k__ from 1 to nops(L_) do\012  s__ := convert(L_[k__],string):\012  if type(L_[k__],indexed) then s__ := cat(s__[1],s__[3..StringTools[Length](s__)-1]) end if:\012  L__ := [op(L__),s__]:\012  end do:\012 map(convert,L__,name):\012 end proc:\012RealList2String := proc(L_) local L__:\012 L__ := RealList2List(L_):\012 cat(op(L__)):\012 end proc:\012FixedPoint := proc(v_) local k__,fix__:\012 fix__ := []:\012 for k__ from 1 to nops(v_) do\012  if v_[k__] = k__ then fix__ := [op(fix__),k__] end if:\012  end do:\012 convert(fix__,set): \012 end proc:\012DeleteByRank := proc(SS_,joklist_,joksign_) local j__,k__,J__:\012 J__ := []: k__ := 1:\012 while k__ &lt;= nops(SS_) do\012  j__ := k__:\012  while evalb(j__ in joklist_) do\012   j__ := j__+1:\012   end do:\012  if j__=k__ then J__ := [op(J__),SS_[j__]]: k__ := j__+1:\012             else J__ := [op(J__),joksign_]: k__ := j__:\012             end if:\012  end do:\012 J__:\012 end proc:\012TypeList := proc(L_,type_) local k__,L__:\012 L__ := []:\012 for k__ from 1 to nops(L_) do \012  if is(L_[k__],type_) then L__ := [op(L__),L_[k__]] end if:\012  end do:\012 L__:\012 end proc:\012                                                                                                          \012rule_nssr := (bb_,i_) -&gt;  [seq(bb_[k__],k__=1..i_-1) , bb_[i_]-1 , seq(bb_[k__],k__=i_+1..nops(bb_)) ]:\012rule_nsar := (bb_,i_) -&gt; bb_:\012rule_tasr := proc(bb_,i_) \012 if i_&gt;1 then [seq(bb_[k__],k__=1..i_-1) , bb_[i_]-1 , seq(bb_[k__],k__=i_+1..nops(bb_))]\012         else [seq(0,k__=1..nops(bb_))]\012         end if:\012 end proc:\012rule_taar := (bb_,i_) -&gt; if i_&gt;1 then bb_ else [seq(0,k__=1..nops(bb_))] end if:\012rule_dec := proc(nr_,B_,N_) local n__,v__,s__,b__,k__:\012 n__ := nr_[1]: \012 v__ := nr2v(nr_,B_):\012 s__ := add(v__[k__]-1,k__=1..nops(v__)):\012 b__ := []:\012 if n__ &lt;= nops(B_)-2 \012  then for k__ from 1 to B_[n__+1] do\012        if s__+k__-1 &gt; N_ then b__ := [op(b__),0] else b__ := [op(b__),1] end if:\012        end do:\012  else for k__ from 1 to B_[n__+1] do\012        if s__+k__-1 &lt;&gt; N_ then b__ := [op(b__),0] else b__ := [op(b__),1] end if:\012        end do:\012  end if:\012\012 b__\012 end proc:\012                                                                                                          \012name_comb_l := proc(ww_,i_,X_) local ww__,p__,joklist__,joksign__: \012 p__ := X_[1]: joklist__ := X_[2]: joksign__ := X_[3]:\012 ww__ := combinat[choose](ww_,p__):\012 ww__ := DeleteByRank(ww__,joklist__,joksign__):\012 [seq(map(swq,ww__[k__]),k__=1..nops(ww__))]:\012 end proc:\012name_perm_l := proc(ww_,i_,X_) local ww__,p__,joklist__,joksign__:\012 p__ := X_[1]: joklist__ := X_[2]: joksign__ := X_[3]:\012 ww__ := combinat[permute](ww_[i_],p__):\012 ww__ := DeleteByRank(ww__,joklist__,joksign__):\012 [seq(map(swq,ww__[k__]),k__=1..nops(ww__))]:\012 end proc:\012name_multiperm_l := proc(n_,ww_,i_,univ_) local mot__,part__,pp__,place__,perm__,k__,ww__,u__,WW__:\012 mot__ := univ_[1]: part__ := univ_[2]:\012 WW__ := []:\012 pp__ := nops(part__[n_]):\012 place__ := [seq(ListTools[Search](c__,mot__),c__ in part__[n_])]:\012 perm__  := name_perm_l([part__[n_]],1,[pp__,{},&quot;&quot;]):\012 ww__ := ww_[i_]:\012 for u__ in perm__ do \012  for k__ from 1 to pp__ do\012   ww__[place__[k__]] := u__[k__]:\012   end do:\012  WW__ := [op(WW__),ww__]:\012  end do:\012\012 WW__:\012 end proc:\012name_dec := proc(M_) local code__,m__,k__:\012 code__ := &quot;&quot;:\012 for k__ from 1 to StringTools[Length](M_) do\012  m__ := parse(M_[k__]):\012  if m__=0 then code__ := cat(code__,&quot; &quot;)\012           else code__ := cat(code__,seq(&quot;X &quot;,k__=1..m__))\012           end if:\012  code__ := cat(code__,&quot;| &quot;):\012 end do:\012 code__[1..StringTools[Length](code__)-1]:\012 end proc:\012                                                                                                          \012event_empty := proc(v_,EVENT_,B_,BB_,WW_)\012 false:\012 end proc:\012event_full := proc(v_,EVENT_,B_,BB_,WW_)\012 true:\012 end proc:\012event_all := proc(v_,EVENT_,B_,BB_,WW_,log_:=`and`) local k__,boo__:\012 boo__ := []:\012 for k__ from 1 to nops(v_) do\012  boo__ := [op(boo__),evalb(WW_[k__][v2nr(v_,B_,k__)[2]]=EVENT_[k__])]:\012  end do:\012 convert(boo__,log_):\012 end proc:\012event_sample := proc(v_,EVENT_,B_,BB_,WW_,log_:=`and`) local k__,boo__:\012 boo__ := []:\012 for k__ from 1 to nops(v_) do\012  boo__ := [op(boo__),evalb(EVENT_[k__] = WW_[k__][v2nr(v_,B_,k__)[2]])]:\012  end do:\012 convert(boo__,log_):\012 end proc:\012event_isin_nset_wset := proc(v_,EVENT_,B_,BB_,WW_,log_:=`or`) local k__,isin__,boo__,EVENT1__:\012 EVENT1__ := EVENT_[1] intersect {seq(k__,k__=1..nops(v_))}:\012 boo__ := []:\012 for k__ from 1 to nops(EVENT1__) do\012  isin__ := EVENT1__[k__]:\012  boo__ := [op(boo__),evalb(WW_[isin__][v2nr(v_,B_,isin__)[2]] in EVENT_[2])]:\012  end do:\012 convert(boo__,log_):\012 end proc:\012event_isin_nseq_wseq := proc(v_,EVENT_,B_,BB_,WW_,log_:=`and`) local k__,isin__,boo__,EVENT1__:\012 EVENT1__ := convert(convert(EVENT_[1],set) intersect {seq(k__,k__=1..nops(v_))},list):\012 boo__ := []:\012 for k__ from 1 to nops(EVENT1__) do \012  isin__ := EVENT1__[k__]:\012  boo__ := [op(boo__),evalb(WW_[isin__][v2nr(v_,B_,isin__)[2]] in EVENT_[2][k__])]:\012  end do:\012 convert(boo__,log_):\012 end proc:\012event_iseq_wone_nany := proc(v_,EVENT_,B_,BB_,WW_,log_:=`or`) local k__,boo__:\012 boo__ := []:\012 for k__ from 1 to nops(v_) do\012  boo__ := [op(boo__),evalb(EVENT_ = WW_[k__][v2nr(v_,B_,k__)[2]])]:\012  end do:\012 convert(boo__,log_):\012 end proc:\012event_isin_wone_nany := proc(v_,EVENT_,B_,BB_,WW_,log_:=`or`) local k__,boo__:\012 boo__ := []:\012 for k__ from 1 to nops(v_) do\012  boo__ := [op(boo__),evalb(EVENT_ in WW_[k__][v2nr(v_,B_,k__)[2]])]:\012  end do:\012 convert(boo__,log_):\012 end proc:\012event_isin_wset_alone := proc(v_,EVENT_,B_,BB_,WW_,log_:=`or`) local b__,k__,l__,set__,boo__:\012 set__ := i__ -&gt; {seq(k__,k__=1..nops(v_))} minus {i__}:\012 boo__  := [seq(true,k__=1..nops(v_))]:\012 for l__ from 1 to nops(v_) do\012  for k__ in set__(l__) do\012    b__ := evalb(not(WW_[k__][v2nr(v_,B_,k__)[2]] in EVENT_)):\012    boo__[l__] := evalb(boo__[l__] and b__):\012    end do:\012   b__ := evalb(WW_[l__][v2nr(v_,B_,l__)[2]] in EVENT_):\012   boo__[l__] := evalb(boo__[l__] and b__):  \012   end do:\012 convert([seq(boo__[l__],l__=1..nops(v_))],log_):\012 end proc:\012event_isin_ww_anywhere := proc(v_,EVENT_,B_,BB_,WW_,log_:=`or`) local k__,boo__:\012 boo__ := []:\012 for k__ from 1 to nops(v_)-1 do\012  boo__ := [op(boo__),evalb(cat(WW_[k__][v2nr(v_,B_,k__)[2]],WW_[k__+1][v2nr(v_,B_,k__+1)[2]]) in EVENT_)]:\012  end do: \012 convert(boo__,log_):\012 end proc:\012event_less_wone_numb := proc(v_,EVENT_,B_,BB_,WW_,log_:=`true`) local w__,n__,vw__,boo__:\012 w__ := EVENT_[1]: n__ := EVENT_[2]:\012 vw__ := PrintW(v_,B_,WW_,'sq'): \012 boo__ := evalb(ListTools[Occurrences](w__,vw__) &lt;= n__):\012 boo__:\012 end proc:\012event_equal_wone_numb := proc(v_,EVENT_,B_,BB_,WW_,log_:=`true`) local w__,n__,vw__,boo__:\012 w__ := EVENT_[1]: n__ := EVENT_[2]:\012 vw__ := PrintW(v_,B_,WW_,'sq'): \012 boo__ := evalb(ListTools[Occurrences](w__,vw__) = n__):\012 boo__:\012 end proc:\012event_more_wone_numb := proc(v_,EVENT_,B_,BB_,WW_,log_:=`true`) local w__,n__,vw__,boo__:\012 w__ := EVENT_[1]: n__ := EVENT_[2]:\012 vw__ := PrintW(v_,B_,WW_,'sq'):\012 boo__ := evalb(ListTools[Occurrences](w__,vw__) &gt;= n__):\012 boo__:\012 end proc:\012event_path_through_each := proc(v_,EVENT_,B_,BB_,WW_,log_:=`and`) local pq__,n__,v__,boo__:\012 pq__ := EVENT_:\012 n__ := [seq(pq__[k__][1]+pq__[k__][2],k__=1..nops(pq__))]:\012 v__ := [seq(v_[1..n__[k__]],k__=1..nops(n__))]: \012 boo__ := [seq(evalb(ListTools[Occurrences](1,v__[k__]) = pq__[k__][1]),k__=1..nops(n__))]:\012 convert(boo__,log_):\012 end proc:\012event_path_side_which := proc(v_,EVENT_,B_,BB_,WW_,log_:=`and`) local test__,boo__:\012 if       EVENT_ = &quot;&gt;&quot;  then test__ := k___ -&gt; evalb(ListTools[Occurrences](2,v_[1..k___]) &gt;  k___/2)\012  else if EVENT_ = &quot;&lt;&quot;  then test__ := k___ -&gt; evalb(ListTools[Occurrences](2,v_[1..k___]) &lt;  k___/2)\012  else if EVENT_ = &quot;&lt;&gt;&quot; then test__ := k___ -&gt; evalb(ListTools[Occurrences](2,v_[1..k___]) &lt;&gt; k___/2)\012  else if EVENT_ = &quot;&gt;=&quot; then test__ := k___ -&gt; evalb(ListTools[Occurrences](2,v_[1..k___]) &gt;= k___/2)\012  else if EVENT_ = &quot;&lt;=&quot; then test__ := k___ -&gt; evalb(ListTools[Occurrences](2,v_[1..k___]) &lt;= k___/2)\012  end if end if end if end if end if:\012 boo__ := [seq(test__(k__),k__=1..nops(v_))]:\012 convert(boo__,log_):\012 end proc:\012event_path_side_end := proc(v_,EVENT_,B_,BB_,WW_,log_:=`and`) local n__,q__,r__,boo1__,boo2__,boo__:\012 n__ := nops(v_):\012 q__ := iquo(n__,2,'r__'): \012 boo1__ := event_path_through_each(v_,[[q__,q__]],B_,BB_,WW_):\012 boo2__ := event_path_side_which(v_[1..n__-1],EVENT_,B_,BB_,WW_):\012 if r__ = 0 then boo__ := boo1__ and boo2__ else boo__ := false end if:\012 boo__:\012 end proc:\012event_fix_equal_set := proc(v_,EVENT_,B_,BB_,WW_,log_:=`true`) local fix__,wfix__,boo__:\012 fix__ := FixedPoint(v_):\012 wfix__ := {seq(WW_[1][k__],k__ in fix__)}:\012 if wfix__ = EVENT_ then boo__ := `true` else boo__ := `false` end if:\012 boo__:\012 end proc:\012event_fix_include_set := proc(v_,EVENT_,B_,BB_,WW_,log_:=`true`) local fix__,wfix__,boo__:\012 fix__ := FixedPoint(v_):\012 wfix__ := {seq(WW_[1][k__],k__ in fix__)}:\012 if EVENT_ subset wfix__ then boo__ := `true` else boo__ := `false` end if:\012 boo__:\012 end proc:\012event_fix_equal_nb := proc(v_,EVENT_,B_,BB_,WW_,log_:=`true`) local fix__,boo__:\012 fix__ := FixedPoint(v_):\012 if nops(fix__) = EVENT_ then boo__ := `true` else boo__ := `false` end if:\012 boo__:\012 end proc:\012event_fix_more_nb := proc(v_,EVENT_,B_,BB_,WW_,log_:=`true`) local fix__,boo__:\012 fix__ := FixedPoint(v_):\012 if nops(fix__) &gt;= EVENT_ then boo__ := `true` else boo__ := `false` end if:\012 boo__:\012 end proc:\012event_strict_increase := proc(v_,EVENT_,B_,BB_,WW_,log_:=`and`) local k__,boo__:\012 boo__ := []:\012 for k__ from 1 to nops(v_)-1 do\012  boo__ := [op(boo__),evalb(WW_[k__][v2nr(v_,B_,k__)[2]] &lt; WW_[k__+1][v2nr(v_,B_,k__+1)[2]])]:\012  end do: \012 convert(boo__,log_):\012 end proc:\012event_isin_wset := proc(v_,EVENT_,B_,BB_,WW_,log_:=`xor`) local k__,nr__,boo__:\012 boo__ := []:\012 nr__ := v2nr(v_,B_):\012 for k__ from 1 to nops(EVENT_) do\012   boo__ := [op(boo__),evalb(EVENT_[k__] in WW_[nr__[1]][nr__[2]])]:\012   end do:\012 convert(boo__,log_):\012 end proc:\012end module:                                                                                                         \012                                                                         \012######################################################## FILM ##################################################################            \012\012PROBI_CO := module()                                                                                      \012\012  uses     DocumentTools, StringTools, ListTools, plots, LinearAlgebra, \012           AnimationII, AlgLin, Analyse, Geometrie, ProbComb, ProbMisc; \012  export   EQperm_E, EQperm_T, EQperm_P,\012           EQarr_E, EQarr_T, EQarr_P,\012           EQcomb_E, EQcomb_T, EQcomb_P,\012           INDepr_E, INDepr_T, INDepr_P,\012           INDwalk_E, INDwalk_T, INDwalk_P,\012           EPRind_E, EPRind_T, EPRind_P;\012  local    Paragraphe;\012  option package;\012\012########################################################\012\012univ := [[1,1,1,1],[&quot;B&quot;,&quot;A&quot;,&quot;N&quot;,&quot;C&quot;]]:                                                                     \012event_i := [[&quot;N&quot;,&quot;B&quot;,&quot;C&quot;,&quot;A&quot;],event_sample,`and`]:                                                         \012event_ii := [[{&quot;B&quot;},{&quot;A&quot;}],event_isin_nset_wset,`or`]:                                                     \012EQperm_E := table([]):                                                                                     \012EQperm_E[&quot;i&quot;] := [4,4,univ,event_i]:                                                                       \012EQperm_E[&quot;ii&quot;] := [4,4,univ,event_ii]:                                                                     \012EQperm_T := &quot;i&quot;:                                                                                           \012EQperm_P := proc(PAR,T) global o0,OPT,AT,CHX:                                                              \012\012JOK := [&quot;#&quot;]:\012\012n := PAR[1]: n := PAR[2]: UNIV := PAR[3]: EVENT := PAR[4]:\012Up := UNIV[1]: Us := UNIV[2]: Ed := EVENT[1]: Er := EVENT[2]: Eb := EVENT[3]:\012if evalb(T = &quot;ii&quot; and member(Ed[1][1],Us,'m')) then Ed := [{m},Ed[2]] end if:\012\012bb := Up: bf := [seq(rule_nssr,k=2..n)]: BF := [bb,op(bf)]:\012ww := Us: wf := [seq((w,i)-&gt;ww,k=2..n)]: WF := [ww,op(wf)]:\012\012B := Range(BF): OO := Node(B,o0,OPT):\012BB := Rule(BF): PP := Prob(BB): WW := Name(WF):\012UU := Universe(B,PP): JU := Joker(B,UU,WW,JOK,OPT):\012EE := Event(B,UU,Ed,Er,BB,WW,Eb): JE := Joker(B,EE,WW,JOK,OPT): \012EEp := PrintEventProb(EE,'pr'): EEs := PrintEventSet(B,EE,WW,'cc'): prE := ProbEvent(EE,'pr'):\012\012if       T=&quot;i&quot;   then P3 := [seq(&quot;&quot;,k=0..n-1),[1,&quot;/&quot;,n,&quot;!&quot;,&quot; = &quot;,prE]]:\012                      W3 := [seq([cat(&quot;L&quot;,k)],k=1..n),&quot;A&quot;]:\012                      PW := Matrix(3,2,[ [PW0,PW0],[PW0,PW0],[PW0,[P3,W3]] ]):\012 else if T=&quot;ii&quot;  then P3 := [seq(&quot;&quot;,k=0..n-1),[n-1,&quot;!&quot;,&quot;/&quot;,n,&quot;!&quot;,&quot; = &quot;,prE]]:\012                      W3 := [seq([cat(&quot;L&quot;,k)],k=1..n),&quot;B&quot;]:\012                      PW := Matrix(3,2,[ [PW0,PW0],[PW0,PW0],[PW0,[P3,W3]] ]):\012                    \012 end if end if:\012if       T=&quot;i&quot;  then PRT := Matrix(3,2,[ [PRTnl,PRTnl],[PRTnn,PRTnc],[PRTnn,PRTii] ])\012 else if T=&quot;ii&quot; then PRT := Matrix(3,2,[ [PRTnl,PRTnl],[PRTnn,PRTnc],[PRTnn,PRTii] ])\012 end if end if:\012TREE := EventTree(B,JU,JE,PP,OO,WW,PW,PRT,CHX,AT,JOK,OPT);\012\012VS2D := table([ &quot;v&quot;=default, &quot;s&quot;=unconstrained, &quot;a&quot;=none ]):\012G := display( [ TREE ], view=VS2D[&quot;v&quot;], scaling = VS2D[&quot;s&quot;], axes = VS2D[&quot;a&quot;] ):\012Calcs := [B,UU,EE]: Graphs := G:\012table([ &quot;c&quot; = Calcs , &quot;g&quot; = Graphs ]):\012\012end proc:\012\012########################################################\012univ_i  := [[3,2],['R'[1],'R'[2],'R'[3],'B'[1],'B'[2]]]:                                                  \012univ_ii := [[1,1,1],[1,2,3]]:                                                                             \012event_i  := [[{1,2,3},{'R'[1],'R'[2],'R'[3]}],event_isin_nset_wset,`and`]:                                \012event_ii := [[{},{}],event_strict_increase,`and`]:                                                        \012EQarr_E := table([]):                                                                                     \012EQarr_E[&quot;i&quot;]  := [3,5,univ_i,event_i]:                                                                    \012EQarr_E[&quot;ii&quot;] := [2,3,univ_ii,event_ii]:                                                                  \012EQarr_T := &quot;i&quot;:                                                                                           \012EQarr_P := proc(PAR,T) global o0,OPT,AT,CHX:                                                              \012\012JOK := [&quot;#&quot;]:\012\012p := PAR[1]: n := PAR[2]: UNIV := PAR[3]: EVENT := PAR[4]:\012Up := UNIV[1]: Us := UNIV[2]: Ed := EVENT[1]: Er := EVENT[2]: Eb := EVENT[3]:\012\012if T=&quot;i&quot; then bb := repeat(n,1) else bb := Up end if: bf := [seq(rule_nssr,k=2..p)]: BF := [bb,op(bf)]:\012ww := Us: wf := [seq((w,i)-&gt;ww,k=2..p)]: WF := [ww,op(wf)]:\012\012B := Range(BF): OO := Node(B,o0,OPT):\012BB := Rule(BF): PP := Prob(BB): WW := Name(WF):\012UU := Universe(B,PP): JU := Joker(B,UU,WW,JOK,OPT):\012EE := Event(B,UU,Ed,Er,BB,WW,Eb): JE := Joker(B,EE,WW,JOK,OPT): \012EEp := PrintEventProb(EE,'pr'): EEs := PrintEventSet(B,EE,WW,'cc'): prE := ProbEvent(EE,'pr'):\012\012A := 'A': C := 'C':\012if       T=&quot;i&quot;  then if p&lt;= Up[1] then P3 := [seq(&quot;&quot;,k=1..p),[A[Up[1]]^p,&quot; / &quot;,A[n]^p,&quot; = &quot;,prE]]\012                                  else P3 := [seq(&quot;&quot;,k=1..p),[&quot;impossible = &quot;,prE]]\012                                  end if:\012                     W3 := [seq([&quot;T&quot;,k],k=1..p),&quot;&quot;]:\012                     PW := Matrix(3,2,[[PW0,PW0],[PW0,PW0],[PW0,[P3,W3]]]):\012 else if T=&quot;ii&quot; then if p&lt;=n then P3 := [seq(&quot;&quot;,k=1..p),[C[n]^p,&quot; / &quot;,A[n]^p,&quot; = &quot;,prE]]\012                             else P3 := [seq(&quot;&quot;,k=1..p),[&quot;impossible = &quot;,prE]]\012                             end if:\012                     W3 := [seq([&quot;T&quot;,k],k=1..p),&quot;&quot;]:\012                     PW := Matrix(3,2,[[PW0,PW0],[PW0,PW0],[PW0,[P3,W3]]]):\012 end if end if:\012if       T=&quot;i&quot;  then PRT := Matrix(3,2,[ [PRTnl,PRTnl],[PRTnn,PRTnc],[PRTii,PRTii] ])\012 else if T=&quot;ii&quot; then PRT := Matrix(3,2,[ [PRTnl,PRTnl],[PRTnn,PRTnc],[PRTii,PRTii] ])\012 end if end if:\012TREE := EventTree(B,JU,JE,PP,OO,WW,PW,PRT,CHX,AT,JOK,OPT);\012\012VS2D := table([ &quot;v&quot;=default, &quot;s&quot;=unconstrained, &quot;a&quot;=none ]):\012G := display( [ TREE ], view=VS2D[&quot;v&quot;], scaling = VS2D[&quot;s&quot;], axes = VS2D[&quot;a&quot;] ):\012Calcs := [B,UU,EE]: Graphs := G:\012table([ &quot;c&quot; = Calcs , &quot;g&quot; = Graphs ]):\012\012end proc:\012\012\012########################################################\012\012univ := [[],{1,2,3,4,5}]:                                                                                                \012event_i  := [3,event_isin_wone_nany,`or`]:                                                                               \012event_ii := [TypeList(univ[2],`even`),event_isin_wset,`xor`]:                                                            \012EQcomb_E := table([]):                                                                                                   \012EQcomb_E[&quot;i&quot;]  := [3,5,univ,event_i]:                                                                                    \012EQcomb_E[&quot;ii&quot;] := [3,5,univ,event_ii]:                                                                                   \012EQcomb_T := &quot;i&quot;:                                                                                                         \012EQcomb_P := proc(PAR,T) global o0,OPT,AT,CHX:                                                                            \012\012JOK := [&quot;#&quot;]:\012\012p := PAR[1]: n := PAR[2]: UNIV := PAR[3]: EVENT := PAR[4]:\012Up := UNIV[1]: Us := UNIV[2]: Ed := EVENT[1]: Er := EVENT[2]: Eb := EVENT[3]:\012cnp := binomial(n,p):\012\012bb := repeat(cnp,1): bf := []: BF := [bb,op(bf)]:\012ww := name_comb_l(Us,'nul',[p,{},JOK]): wf := []: WF := [ww,op(wf)]:\012\012B := Range(BF): OO := Node(B,o0,OPT):\012BB := Rule(BF): PP := Prob(BB): WW := Name(WF):\012UU := Universe(B,PP): JU := Joker(B,UU,WW,JOK,OPT):\012EE := Event(B,UU,Ed,Er,BB,WW,Eb): JE := Joker(B,EE,WW,JOK,OPT): \012EEp := PrintEventProb(EE,'pr'): EEs := PrintEventSet(B,EE,WW,'la'): prE := ProbEvent(EE,'pr'):\012\012C := 'C':\012if       T=&quot;i&quot;  then P3 := [&quot;&quot;,[C[n-1]^(p-1),&quot; / &quot;,C[n]^p,&quot; = &quot;,prE]]:\012                     W3 := [&quot;&quot;,&quot;A&quot;]:\012                     PW := Matrix(3,2,[[PW0,PW0],[PW0,PW0],[[P0,W0],[P3,W3]]]):\012 else if T=&quot;ii&quot; then n1 := nops(Ed): \012                     if evalb(p&lt;=n and n1&gt;0 and p-1&lt;=n-n1) \012                      then P3 := [&quot;&quot;,[C[n1]^1,&quot; x &quot;,C[n-n1]^(p-1),&quot; / &quot;,C[n]^p,&quot; = &quot;,prE]]\012                      else P3 := [&quot;&quot;,[&quot;impossible = &quot;,prE]]\012                      end if:\012                     W3 := [&quot;&quot;,&quot;B&quot;]:\012                     PW := Matrix(3,2,[[PW0,PW0],[PW0,PW0],[[P0,W0],[P3,W3]]]):\012 end if end if:\012if       T=&quot;i&quot;  then PRT := Matrix(3,2,[ [PRTnl,PRTnl],[PRTnn,PRTnl],[PRTii,PRTii] ])\012 else if T=&quot;ii&quot; then PRT := Matrix(3,2,[ [PRTnl,PRTnl],[PRTnn,PRTnl],[PRTii,PRTii] ])\012 end if end if:\012TREE := EventTree(B,JU,JE,PP,OO,WW,PW,PRT,CHX,AT,JOK,OPT):\012\012VS2D := table([ &quot;v&quot;=default, &quot;s&quot;=unconstrained, &quot;a&quot;=none ]):\012G := display( [ TREE ], view=VS2D[&quot;v&quot;], scaling = VS2D[&quot;s&quot;], axes = VS2D[&quot;a&quot;] ):\012Calcs := [B,UU,EE]:\012Graphs := G:\012table([ &quot;c&quot; = Calcs , &quot;g&quot; = Graphs ]):\012\012end proc:\012\012########################################################\012\012univ := [[[70,30],[90,10],[80,20]],[seq(['E'[k],'E'[k]^'c'],k=1..3)]]:                                    \012event_i  := [[seq('E'[k],k=1..3)],event_all,`and`]:                                                       \012event_ii := [[seq('E'[k]^'c',k=1..3)],event_all,`and`]:                                                   \012INDepr_E := table([]):                                                                                    \012INDepr_E[&quot;i&quot;]  := [3,[2,2,2],univ,event_i]:                                                               \012INDepr_E[&quot;ii&quot;] := [3,[2,2,2],univ,event_ii]:                                                              \012INDepr_T := &quot;i&quot;:                                                                                          \012INDepr_P := proc(PAR,T) global o0,AT,OPT,CHX:                                                             \012\012JOK := [&quot;#&quot;]:\012\012p := PAR[1]: nn := PAR[2]: UNIV := PAR[3]: EVENT := PAR[4]:\012Up := UNIV[1]: Us := UNIV[2]: Ed := EVENT[1]: Er := EVENT[2]: Eb := EVENT[3]:\012\012bb := Up[1]: bf := [seq(unapply(Up[k],b,i),k=2..p)]: BF := [bb,op(bf)]:\012ww := Us[1]: wf := [seq(unapply(Us[k],w,i),k=2..p)]: WF := [ww,op(wf)]:\012\012B := Range(BF): OO := Node(B,o0,OPT):\012BB := Rule(BF): PP := Prob(BB): WW := Name(WF):\012UU := Universe(B,PP): JU := Joker(B,UU,WW,JOK,OPT):\012EE := Event(B,UU,Ed,Er,BB,WW,Eb): JE := Joker(B,EE,WW,JOK,OPT): \012EEp := PrintEventProb(EE,'pr'): EEs := PrintEventSet(B,EE,WW,'cc'): prE := ProbEvent(EE,'pr'):\012\012if       T=&quot;i&quot;   then P3 := [seq(&quot;&quot;,k=1..p),[prE,&quot; = &quot;,evalf(prE)]]:\012                      W3 := [seq([&quot;E&quot;,k],k=1..p),&quot;S\303\251rie&quot;]:\012                      PW := Matrix(3,2,[[PW0,PW0],[PW0,PW0],[PW0,[P3,W3]]]):\012 else if T=&quot;ii&quot;  then P3 := [seq(&quot;&quot;,k=1..p),[prE,&quot; = &quot;,evalf(prE)]]:\012                      W3 := [seq([&quot;E&quot;,k],k=1..p),&quot;Parall\303\250le&quot;]:\012                      PW := Matrix(3,2,[[PW0,PW0],[PW0,PW0],[PW0,[P3,W3]]]):\012 end if end if:\012if       T=&quot;i&quot;   then PRT := Matrix(3,2,[ [PRTpl,PRTpl],[PRTnn,PRTnc],[PRTii,PRTii] ])\012 else if T=&quot;ii&quot;  then PRT := Matrix(3,2,[ [PRTpl,PRTpl],[PRTnn,PRTnc],[PRTii,PRTii] ])\012 end if end if:\012TREE := EventTree(B,JU,JE,PP,OO,WW,PW,PRT,CHX,AT,JOK,OPT);\012\012VS2D := table([ &quot;v&quot;=default, &quot;s&quot;=unconstrained, &quot;a&quot;=none ]):\012G := display( [ TREE ], view=VS2D[&quot;v&quot;], scaling = VS2D[&quot;s&quot;], axes = VS2D[&quot;a&quot;] ):\012Calcs := [B,UU,EE]: Graphs := G:\012table([ &quot;c&quot; = Calcs , &quot;g&quot; = Graphs ]):\012\012end proc:\012\012########################################################\012\012univ := [[40,60],[&quot;O&quot;,&quot;N&quot;]]:                                                                                                  \012event_i := [[[3,3]],event_path_through_each,`and`]:                                                                         \012INDwalk_E := table([]):                                                                                                     \012INDwalk_E[&quot;i&quot;]  := [6,'nul',univ,event_i]:                                                                                  \012INDwalk_T := &quot;i&quot;:                                                                                                           \012INDwalk_P := proc(PAR,T) global o0,OPT,AT,CHX:                                                                              \012\012JOK := [&quot;&quot;]: CHX1 := {1}: OPT1 := copy(OPT): OPT1[&quot;ij&quot;] := [1,1]: OPT1[&quot;mo&quot;] := &quot;P&quot;:\012\012n := PAR[1]: p := PAR[2]: UNIV := PAR[3]: EVENT := PAR[4]:\012Up := UNIV[1]: Us := UNIV[2]: Ed := EVENT[1]: Er := EVENT[2]: Eb := EVENT[3]:\012\012bb := Up: bf := [seq(rule_nsar,k=2..n)]: BF := [bb,op(bf)]:\012ww := Us: wf := [seq((w,i) -&gt; w,k=2..n)]: WF := [ww,op(wf)]:\012\012B := Range(BF): OO := Node(B,o0,OPT1): \012BB := Rule(BF): PP := Prob(BB): WW := Name(WF):\012UU := Universe(B,PP): JU := Joker(B,UU,WW,JOK,OPT1):\012EE := Event(B,UU,Ed,Er,BB,WW,Eb): JE := Joker(B,EE,WW,JOK,OPT1): \012EEp := PrintEventProb(EE,'no'): EEs := PrintEventSet(B,EE,WW,'cc'): prE := ProbEvent(EE,'pr'):\012\012if       T=&quot;i&quot;  then PW := Matrix(3,2,[[PW0,PW0],[PW0,PW0],[PW1(n+1),PW0]])\012 else if T=&quot;ii&quot; then PW := Matrix(3,2,[[PW0,PW0],[PW0,PW0],[PW0,PW0]])\012 end if end if:\012if       T=&quot;i&quot;  then PRT := Matrix(3,2,[[PRTnl,PRTnl],[PRTnn,PRTnn],[PRTni,PRTni]])\012 else if T=&quot;ii&quot; then PRT := Matrix(3,2,[[PRTnl,PRTnl],[PRTnn,PRTnn],[PRTni,PRTni]])\012 end if end if:\012TREE := EventPath(B,JU,JE,PP,OO,WW,PW,PRT,CHX1,AT,JOK,OPT1);\012\012VS2D := table([ &quot;v&quot;=default, &quot;s&quot;=constrained, &quot;a&quot;=none ]):\012G := display( [ TREE ], view=VS2D[&quot;v&quot;], scaling = VS2D[&quot;s&quot;], axes = VS2D[&quot;a&quot;] ):\012Calcs := [B,UU,EE,prE]:\012Graphs := G:\012table([ &quot;c&quot; = Calcs , &quot;g&quot; = Graphs ]):\012\012end proc:\012\012########################################################\012\012univ_i   := [[1,1,1,1],[1,2,3,4]]:                                                                        \012univ_ii  := [[3,1],['R'[1],'R'[2],'R'[3],'B']]:                                                           \012univ_iii := [[3,1],['R','B']]:                                                                            \012event_i   := [[{},{}],event_empty,&quot;&quot;]:                                                                    \012event_ii  := [[{1,2},{'R'[1],'R'[2],'R'[3]}],event_isin_nset_wset,`and`]:                                 \012event_iii := [[{1,2},{'R'}],event_isin_nset_wset,`and`]:                                                  \012EPRind_E := table([]):                                                                                    \012EPRind_E[&quot;i&quot;]   := [2,4,univ_i,event_i]:                                                                  \012EPRind_E[&quot;ii&quot;]  := [2,4,univ_ii,event_ii]:                                                                \012EPRind_E[&quot;iii&quot;] := [2,2,univ_iii,event_iii]:                                                              \012EPRind_T := &quot;i&quot;:                                                                                          \012EPRind_P := proc(PAR,T) global o0,AT,OPT,CHX:                                                             \012\012JOK := [&quot;#&quot;]:\012\012p := PAR[1]: n := PAR[2]: UNIV := PAR[3]: EVENT := PAR[4]:\012Up := UNIV[1]: Us := UNIV[2]: Ed := EVENT[1]: Er := EVENT[2]: Eb := EVENT[3]:\012\012if T=&quot;ii&quot; then bb := repeat(n,1) else bb := Up end if: bf := [seq((b,i)-&gt;bb,k=2..p)]: BF := [bb,op(bf)]:\012ww := Us: wf := [seq((w,i)-&gt;ww,k=2..p)]: WF := [ww,op(wf)]:\012\012B := Range(BF): OO := Node(B,o0,OPT):\012BB := Rule(BF): PP := Prob(BB): WW := Name(WF):\012UU := Universe(B,PP): JU := Joker(B,UU,WW,JOK,OPT):\012EE := Event(B,UU,Ed,Er,BB,WW,Eb): JE := Joker(B,EE,WW,JOK,OPT): \012EEp := PrintEventProb(EE,'pr'): EEs := PrintEventSet(B,EE,WW,'cc'): prE := ProbEvent(EE,'pr'):\012\012if       T=&quot;i&quot;   then P3 := [seq(&quot;&quot;,k=1..p),&quot;&quot;]:\012                      W3 := [seq([&quot;L&quot;,k],k=1..p),Omega]:\012                      PW := Matrix(3,2,[[PW0,PW0],[PW0,PW0],[[P3,W3],PW0]]):\012 else if T=&quot;ii&quot;  then P3 := [seq(&quot;&quot;,k=1..p),[PrintI(&quot;(n-1)^p/n^p&quot;),&quot; = &quot;,prE]]:\012                      W3 := [seq([&quot;T&quot;,k],k=1..p),&quot;A&quot;]:\012                      PW := Matrix(3,2,[[PW0,PW0],[PW0,PW0],[PW0,[P3,W3]]]):\012 else if T=&quot;iii&quot; then P3 := [seq(&quot;&quot;,k=1..p),[PrintI(&quot;[(n-1)/n]^p&quot;),&quot; = &quot;,prE]]:\012                      W3 := [seq([&quot;T&quot;,k],k=1..p),&quot;A&quot;]:\012                      PW := Matrix(3,2,[[PW0,PW0],[PW0,PW0],[PW0,[P3,W3]]]):\012 end if end if end if:\012if       T=&quot;i&quot;   then PRT := Matrix(3,2,[ [PRTpl,PRTpl],[PRTpc,PRTnn],[PRTii,PRTii] ])\012 else if T=&quot;ii&quot;  then PRT := Matrix(3,2,[ [PRTnl,PRTnl],[PRTnn,PRTnc],[PRTii,PRTii] ])\012 else if T=&quot;iii&quot; then PRT := Matrix(3,2,[ [PRTpl,PRTpl],[PRTnn,PRTpc],[PRTii,PRTii] ])\012 end if end if end if:\012TREE := EventTree(B,JU,JE,PP,OO,WW,PW,PRT,CHX,AT,JOK,OPT);\012\012VS2D := table([ &quot;v&quot;=default, &quot;s&quot;=unconstrained, &quot;a&quot;=none ]):\012G := display( [ TREE ], view=VS2D[&quot;v&quot;], scaling = VS2D[&quot;s&quot;], axes = VS2D[&quot;a&quot;] ):\012Calcs := [B,UU,EE]: Graphs := G:\012table([ &quot;c&quot; = Calcs , &quot;g&quot; = Graphs ]):\012\012end proc:\012\012end module:                                                                                                                                                                                                                                                                                                                          \012\012####################################################### GESTION  ###############################################################\012with(DocumentTools): with(StringTools): with(ListTools): with(plots): with(LinearAlgebra):                                 \012with(AnimationII): with(AlgLin): with(Analyse): with(Geometrie): with(ProbComb): with(ProbMisc):\012################################################################################################################################\012with(PROBI_CO):\012\012col1 := [[&quot;IndianRed&quot;,&quot;LightPink&quot;,&quot;DarkRed&quot;],[&quot;SteelBlue&quot;,&quot;LightSteelBlue&quot;,&quot;DarkBlue&quot;]]:\012col2 := col1:\012col3 := col1:\012COL := Matrix(3,2,[col1,col2,col3]):\012\012sty1 := [['solid',0,'nul'],['solid',1,'nul']]:\012sty2 := [['dot',0,'right'],['dot',1,'right']]:\012sty3 := [['dash',0,'nul'],['dash',1,'nul']]:\012STY := Matrix(3,2,[sty1,sty2,sty3]):\012\012fss1 := [[[ROMAN,9],[ROMAN,6]],[[ROMAN,9],[ROMAN,6]]]:\012fss2 := fss1:\012fss3 := [[[ROMAN,9],[ROMAN,9]],[[ROMAN,9],[ROMAN,9]]]:\012FSS := Matrix(3,2,[fss1,fss2,fss3]):\012\012AT  := Matrix(3,2,(i,j)-&gt;[COL[i,j],STY[i,j],FSS[i,j]]):\012HL := [[&quot;Crimson&quot;,'solid',1],[&quot;BlueViolet&quot;,'solid',1]]:\012\012IJ := [2,8]: EPS := 0.05: HSPACE := 1.5: VSPACE := 1: BREAK := 3: MODE := &quot;T&quot;:\012OPT := table([ &quot;ij&quot; = IJ, &quot;eps&quot; = EPS, &quot;hs&quot; = HSPACE, &quot;vs&quot; = VSPACE, &quot;br&quot; = BREAK, &quot;mo&quot; = MODE ]): \012CHX := {1,2,3}:\012\012o0 := [0,0]:\012\012########################################################\012#EQ\012##perm\012T0 := &quot;i&quot;:\012PAR := EQperm_E[T0]: n0 := PAR[1]: n0 := PAR[2]: UNIV := PAR[3]: EVENT := PAR[4]:\012Do(%eqTAR1i_1 = cat(op(UNIV[2]))):\012Do(%eqTAR1i_2 = cat(op(EVENT[1]))):\012\012T0 := &quot;ii&quot;:\012PAR := EQperm_E[T0]: n0 := PAR[1]: n0 := PAR[2]: UNIV := PAR[3]: EVENT := PAR[4]:\012Do(%eqTAR1ii_1 = cat(op(UNIV[2]))):\012Do(%eqTAR1ii_2 = cat(op(EVENT[1][2]))):\012\012##arr\012T0 := &quot;i&quot;:\012PAR := EQarr_E[T0]: p0 := PAR[1]: n0 := PAR[2]: UNIV := PAR[3]: EVENT := PAR[4]:\012Do(%eqTAR2i_1 = p0):\012Do(%eqTAR2i_2 = UNIV[1]):\012\012T0 := &quot;ii&quot;:\012PAR := EQarr_E[T0]: p0 := PAR[1]: n0 := PAR[2]: UNIV := PAR[3]: EVENT := PAR[4]:\012Do(%eqTAR2ii_1 = p0):\012Do(%eqTAR2ii_2 = UNIV[2]):\012\012##COMB\012T0 := &quot;i&quot;:\012PAR := EQcomb_E[T0]: p0 := PAR[1]: n0 := PAR[2]: UNIV := PAR[3]: EVENT := PAR[4]:\012Do(%eqTAR3i_1 = p0):\012Do(%eqTAR3i_2 = UNIV[2]):\012Do(%eqTAR3i_3 = EVENT[1]):\012\012T0 := &quot;ii&quot;:\012PAR := EQcomb_E[T0]: p0 := PAR[1]: n0 := PAR[2]: UNIV := PAR[3]: EVENT := PAR[4]:\012Do(%eqTAR3ii_1 = p0):\012Do(%eqTAR3ii_2 = UNIV[2]):\012\012##\012Do(%eqRAB0 = true):\012Do(%eqPLS1 = EP2D):\012########################################################\012#IND\012##epr\012T0 := &quot;i&quot;:\012PAR := INDepr_E[T0]: p0 := PAR[1]: nn := PAR[2]: UNIV := PAR[3]: EVENT := PAR[4]:\012ss := [seq(add(UNIV[1][k0][l0],l0=1..nops(UNIV[1][k0])),k0=1..p0)]:\012Do(%indTAR2i_1 = p0):\012Do(%indTAR2i_2 = [seq(UNIV[1][k0][2],k0=1..p0)]):\012\012T0 := &quot;ii&quot;:\012PAR := INDepr_E[T0]: p0 := PAR[1]: nn := PAR[2]: UNIV := PAR[3]: EVENT := PAR[4]:\012Do(%indTAR2ii_1 = p0):\012Do(%indTAR2ii_2 = [seq(UNIV[1][k0][2],k0=1..p0)]):\012\012##walk\012T0 := &quot;i&quot;:\012PAR := INDwalk_E[T0]: n0 := PAR[1]: UNIV := PAR[3]: EVENT := PAR[4]:\012Do(%indTAR3_1 = n0/2):\012Do(%indTAR3_2 = UNIV[1][1]):\012\012##\012Do(%indRAB0 = true):\012Do(%indPLS1 = EP2D):\012########################################################\012#EPR\012##ind\012T0 := &quot;i&quot;:\012PAR := EPRind_E[T0]: p0 := PAR[1]: n0 := PAR[2]: UNIV := PAR[3]: EVENT := PAR[4]:\012Do(%eprTAR1_1 = p0):\012Do(%eprTAR1_2 = n0):\012\012T0 := &quot;ii&quot;:\012PAR := EPRind_E[T0]: p0 := PAR[1]: n0 := PAR[2]: UNIV := PAR[3]: EVENT := PAR[4]:\012Do(%eprTAR2i_1 = p0):\012Do(%eprTAR2i_2 = UNIV[1]):\012\012T0 := &quot;iii&quot;:\012PAR := EPRind_E[T0]: p0 := PAR[1]: n0 := PAR[2]: UNIV := PAR[3]: EVENT := PAR[4]:\012Do(%eprTAR2ii_1 = p0):\012Do(%eprTAR2ii_2 = UNIV[1]):\012\012##\012Do(%eprRAB0 = true):\012Do(%eprPLS1 = EP2D):\012"/>
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<Input><Text-field style="Text" bold="true" foreground="[255,102,0]" size="16" layout="Normal" alignment="centred"><Font size="20" bold="true" foreground="[255,102,0]">Probabilidades I</Font></Text-field>
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<Input><Text-field style="Text" foreground="[255,102,0]" italic="true" size="16" layout="Normal" alignment="centred"><Font size="12" foreground="[255,102,0]" encoding="UTF-8" italic="true">Cursos e Exerc\303\255cios</Font></Text-field>
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<Input><Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"><Font size="10" encoding="UTF-8" italic="true">Os links de exerc\303\255cios do WIMS se referem a uma compila\303\247\303\243o de exerc\303\255cios no site do WIMS, desenvolvido por XIAO Gang da Universidade de Nice.</Font></Text-field>
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<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 1" layout="Heading 1" alignment="centred">Aulas</Text-field></Title>
<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field bookmark="co1" style="Heading 1" size="10" layout="Heading 1"><Font size="16" encoding="UTF-8">1. Espa\303\247o probabilizado finito</Font></Text-field></Title>
<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field bookmark="co11" style="Heading 2" size="10" layout="Heading 2"><Font size="14">1.1. Lei da probabilidade</Font></Text-field></Title><Table visible="true" editable="true" exterior="none" pagebreak="cell" showlabel="true" title="" plotalignlists="" hiddenborderdisplay="worksheet" interior="group" postexecute="insert" drawcaption="false" width="1064.0" captionalignment="0" showinput="true" captionposition="1" id="Table4" alignment="left" randomized="false" labelreference="L173397" showgroup="true" order="row"><Table-Column weight="100" separator="true"></Table-Column><Table-Row align="top" separator="true"><Table-Cell padding="5" visible="true" fillcolor="[255,255,255]" rowspan="1" backgroundstyle="0" columnspan="1"><Presentation-Block>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Consideramos um conjunto finito \316\251, chamado universo: os elementos de </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEpJiM1ODUzOTtGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYmLUYsNiNRIUYnLUkobWZlbmNlZEdGJDYlLUYjNiktRiw2J1EnJiM5Mzc7RicvRjBGNEYyLyU2c2VsZWN0aW9uLXBsYWNlaG9sZGVyR0YxL0Y2USdub3JtYWxGJ0YvLyUrZm9yZWdyb3VuZEdRK1swLDE2MCw4MF1GJ0YyLyUscGxhY2Vob2xkZXJHRjFGRkY1RjJGSEYyRkhGOkYyRkg=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEpJiM1ODUzOTtGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYmLUYsNiNRIUYnLUkobWZlbmNlZEdGJDYlLUYjNiktRiw2J1EnJiM5Mzc7RicvRjBGNEYyLyU2c2VsZWN0aW9uLXBsYWNlaG9sZGVyR0YxL0Y2USdub3JtYWxGJ0YvLyUrZm9yZWdyb3VuZEdRK1swLDE2MCw4MF1GJ0YyLyUscGxhY2Vob2xkZXJHRjFGRkY1RjJGSEYyRkhGOkYyRkg=</Equation><Font encoding="UTF-8"> s\303\243o chamados de eventos.
Os eventos</Font> <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn</Equation> e <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiQkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiQkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn</Equation><Font encoding="UTF-8"> dizem ser incompat\303\255veis se </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbWlHRiQ2JlEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEifkYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTi1GOTYuUS8mSW50ZXJzZWN0aW9uO0YnRjJGPEY+RkAvRkNGMUZERkYvRklGMUZKRkwvRlBRLDAuMTY2NjY2N2VtRidGOC1GLDYmUSJCRidGL0YyRjUtRjk2LlEiPUYnRjJGPEY+RkBGQkZERkZGSEZKL0ZNUSwwLjI3Nzc3NzhlbUYnL0ZQRmluLUY5Ni5RLSZ2YXJub3RoaW5nO0YnRjJGPEY+RkBGQkZERkZGSEZKRkxGT0YyRjw=">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</Equation> .</Text-field>
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<Input><Text-field style="Text" layout="Normal">Singletons <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JkYrLUkobWZlbmNlZEdGJDYnLUYjNiktRiw2J1EnJiM5Njk7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGOy8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdRJXRydWVGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvRjpGQC8lK2ZvcmVncm91bmRHUStbMCwxNjAsODBdRidGPC8lLHBsYWNlaG9sZGVyR0ZARj4vRkJRJ2l0YWxpY0YnRjxGQS8lJW9wZW5HUSkmbGJyYWNlO0YnLyUmY2xvc2VHUSkmcmJyYWNlO0YnRjxGQUYrRjxGQQ==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JkYrLUkobWZlbmNlZEdGJDYnLUYjNiktRiw2J1EnJiM5Njk7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGOy8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdRJXRydWVGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvRjpGQC8lK2ZvcmVncm91bmRHUStbMCwxNjAsODBdRidGPC8lLHBsYWNlaG9sZGVyR0ZARj4vRkJRJ2l0YWxpY0YnRjxGQS8lJW9wZW5HUSkmbGJyYWNlO0YnLyUmY2xvc2VHUSkmcmJyYWNlO0YnRjxGQUYrRjxGQQ==</Equation><Font encoding="UTF-8"> s\303\243o chamados eventos elementares: vamos anot\303\241-los <Font foreground="[51,51,51]">\317\211 exceto ambiguidade.</Font></Font></Text-field>
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<Input><Text-field style="Text" layout="Normal">Em cada evento <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn</Equation><Font encoding="UTF-8"> n\303\263s associamos um verdadeiro  </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KFEjcHJGJy8lJWJvbGRHUSV0cnVlRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGOS1JKG1mZW5jZWRHRiQ2JS1GIzYlLUYsNiZRIkFGJy9GM0YxRjUvRjhRJ2l0YWxpY0YnRjUvRjhRJ25vcm1hbEYnRjVGR0Y1Rkc=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KFEjcHJGJy8lJWJvbGRHUSV0cnVlRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGOS1JKG1mZW5jZWRHRiQ2JS1GIzYlLUYsNiZRIkFGJy9GM0YxRjUvRjhRJ2l0YWxpY0YnRjUvRjhRJ25vcm1hbEYnRjVGR0Y1Rkc=</Equation><Font encoding="UTF-8">  e assumimos que os seguintes axiomas s\303\243o verificados:</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font bold="true">PR1</Font> : Para todo <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn</Equation> temos</Text-field>
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<Input><Text-field style="Text" layout="Normal" alignment="centred">  <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> .</Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font bold="true">PR2</Font> : Temos  </Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font bold="true">PR3</Font> : Para qualquer casal <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYlLUYjNictSSNtaUdGJDYmUSJBRicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYuUSIsRidGNy9GO1Enbm9ybWFsRicvJSZmZW5jZUdGOS8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0Y5LyUqc3ltbWV0cmljR0Y5LyUobGFyZ2VvcEdGOS8lLm1vdmFibGVsaW1pdHNHRjkvJSdhY2NlbnRHRjkvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYmUSJCRidGNEY3RjpGN0ZBRjdGQUY3RkE=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYlLUYjNictSSNtaUdGJDYmUSJBRicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYuUSIsRidGNy9GO1Enbm9ybWFsRicvJSZmZW5jZUdGOS8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0Y5LyUqc3ltbWV0cmljR0Y5LyUobGFyZ2VvcEdGOS8lLm1vdmFibGVsaW1pdHNHRjkvJSdhY2NlbnRHRjkvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYmUSJCRidGNEY3RjpGN0ZBRjdGQUY3RkE=</Equation><Font encoding="UTF-8"> de eventos incompat\303\255veis que temos</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">A aplica\303\247\303\243o  </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font encoding="UTF-8"> \303\251 chamado a lei da probabilidade em \316\251 , e o trig\303\252meo </Font><Equation executable="false" style="2D Math" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYlLUYjNi8tSSNtaUdGJDYmUScmIzkzNztGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJStleGVjdXRhYmxlR0Y2LyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi5RIn5GJ0Y3RjkvJSZmZW5jZUdGNi8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0Y2LyUqc3ltbWV0cmljR0Y2LyUobGFyZ2VvcEdGNi8lLm1vdmFibGVsaW1pdHNHRjYvJSdhY2NlbnRHRjYvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZQLUY9Ni5RIixGJ0Y3RjlGQC9GQ1EldHJ1ZUYnRkRGRkZIRkpGTEZOL0ZSUSwwLjMzMzMzMzNlbUYnRjwtRjE2JlEnJlBzY3I7RicvRjVGV0Y3L0Y6USdpdGFsaWNGJy1GLDYlLUYjNiUtRjE2J1EoJk9tZWdhO0YnRjRGNy8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdGV0Y5RjdGOUY3RjlGPEZTRjwtRjE2KFEjcHJGJy8lJWJvbGRHRldGNEY3L0Y6USVib2xkRicvJStmb250d2VpZ2h0R0Zpby1GPTYwRj9GZm9GN0Zob0Zqb0ZARkJGREZGRkhGSkZMRk5GUUY3RjlGN0Y5RjdGOQ==</Equation><Font encoding="UTF-8"> \303\251 chamado espa\303\247o probabilizado.</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal">Evento <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn</Equation><Font encoding="UTF-8"> \303\251 dito ser imposs\303\255veli </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2KFEjcHJGJy8lJWJvbGRHUSV0cnVlRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGOS1JKG1mZW5jZWRHRiQ2JS1GIzYlLUYsNiZRIkFGJy9GM0YxRjUvRjhRJ2l0YWxpY0YnRjUvRjhRJ25vcm1hbEYnRjVGRy1JI21vR0YkNi5RIj1GJ0Y1RkcvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0Znbi1JI21uR0YkNiVRIjBGJ0Y1RkdGNUZH">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</Equation> ,claro se <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>.</Text-field>
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<Input><Text-field style="Text" layout="Normal">1. Para todos os eventos <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn</Equation> e <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiQkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiQkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn</Equation> temos :</Text-field>
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<Input><Text-field style="Text" layout="Normal">(i) Mudando para complementar.</Text-field>
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<Input><Text-field style="Text" layout="Normal" alignment="centred"> <Equation executable="false" style="2D Math" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbWlHRiQ2KFEjcHJGJy8lJWJvbGRHUSV0cnVlRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGOS1JKG1mZW5jZWRHRiQ2JS1GIzYlLUkmbW92ZXJHRiQ2JS1GIzYpLUYsNiZRIkFGJy9GM0YxRjUvRjhRJ2l0YWxpY0YnRkkvJStmb3JlZ3JvdW5kR1ErWzAsMTYwLDgwXUYnRjUvJSxwbGFjZWhvbGRlckdGMS8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdGMUZKLUkjbW9HRiQ2L1EqJk92ZXJCYXI7RidGNUZPL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmdW5zZXRGJy8lKnNlcGFyYXRvckdGZW4vJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGZW4vJShsYXJnZW9wR0Zlbi8lLm1vdmFibGVsaW1pdHNHRmVuLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGZG9GYG9GNUZXRjVGVy1GVDYuUSI9RidGNUZXL0ZaRjQvRmduRjQvRmluRjQvRltvRjQvRl1vRjQvRl9vRjQvRmFvRjQvRmNvUSwwLjI3Nzc3NzhlbUYnL0Zmb0ZicC1JI21uR0YkNiVRIjFGJ0Y1RlctRlQ2LlEoJm1pbnVzO0YnRjVGV0Zqb0ZbcEZccEZdcEZecEZfcEZgcC9GY29RLDAuMjIyMjIyMmVtRicvRmZvRlxxRistRj02Ji1GIzYmRkZGSUY1RkpGSUY1RkpGNUZX</Equation> .</Text-field>
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<Input><Text-field style="Text" foreground="[51,51,51]" layout="Normal"><Font foreground="[51,51,51]" encoding="UTF-8">Se tivermos a escolha, normalmente preferimos considerar apenas os eventos poss\303\255veis, portanto, suponha que </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font foreground="[51,51,51]"> para todo </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1Eia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRK1s1MSw1MSw1MV1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YyRjUvRjlRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1Eia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRK1s1MSw1MSw1MV1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YyRjUvRjlRJ25vcm1hbEYn</Equation><Font foreground="[51,51,51]" encoding="UTF-8"> : mas pode ser conveniente, em alguns casos, incluir eventos imposs\303\255veis.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" foreground="[0,51,0]" encoding="UTF-8">Um teste (ou experi\303\252ncia) </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiRUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiRUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> gera um n\303\272mero finito de poss\303\255veis resultados (ou resultados), observados </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8">  : toda a sua forma do universo \316\251.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" foreground="[0,51,0]">Um evento relacionado a </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2KFEiRUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjJGNUY4Rjs=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2KFEiRUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjJGNUY4Rjs=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> \303\251 um subconjunto </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiQUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiQUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]"> de resultados: dizemos que </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiQUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiQUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> \303\251 alcan\303\247ado quando o resultado do experimento pertence a </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiQUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiQUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]">.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" foreground="[0,51,0]" encoding="UTF-8">Os eventos mais comuns s\303\243o os seguintes: anagramas, jogadas, distribui\303\247\303\265es, empates.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" bold="true" foreground="[0,51,0]">1. Um exemplo abstrato a priori.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" bold="true" foreground="[0,51,0]" encoding="UTF-8">(i) Jogamos um dado manipulado com 4 faces numeradas 1,2,3,4. A probabilidade de atingir 4 \303\251 duas vezes a probabilidade de atingir 3, as probabilidades de atingir 1 ou 2 s\303\243o iguais e duas vezes menores que a atingir 3.
</Font><Font size="10" foreground="[0,51,0]" encoding="UTF-8">O universo \303\251 naturalmente</Font><Font size="10" foreground="[0,51,0]"> </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8">. N\303\263s colocamos </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> e traduzimos a declara\303\247\303\243o por</Font></Text-field>
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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" foreground="[0,51,0]" encoding="UTF-8">A restri\303\247\303\243o </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" foreground="[0,51,0]"> escrevemos </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> , ent\303\243o temos a lei</Font></Text-field>
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O universo pode ser representado por </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> e a lei da probabilidade \303\251 dada por</Font></Text-field>
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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" foreground="[0,51,0]" encoding="UTF-8">Estamos interessados \342\200\213\342\200\213no evento </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2KFEiQ0YnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNjBRIj1GJ0YvRjVGOC9GPFEnbm9ybWFsRicvJSZmZW5jZUdGOi8lKnNlcGFyYXRvckdGOi8lKXN0cmV0Y2h5R0Y6LyUqc3ltbWV0cmljR0Y6LyUobGFyZ2VvcEdGOi8lLm1vdmFibGVsaW1pdHNHRjovJSdhY2NlbnRHRjovJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZURi9GNUY4RkI=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2KFEiQ0YnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNjBRIj1GJ0YvRjVGOC9GPFEnbm9ybWFsRicvJSZmZW5jZUdGOi8lKnNlcGFyYXRvckdGOi8lKXN0cmV0Y2h5R0Y6LyUqc3ltbWV0cmljR0Y6LyUobGFyZ2VvcEdGOi8lLm1vdmFibGVsaW1pdHNHRjovJSdhY2NlbnRHRjovJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZURi9GNUY4RkI=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8">&quot;o comprimento da palavra \303\251 maior ou igual a 5 ou cont\303\251m a letra u &quot;.
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<Input><Text-field style="Text" bold="true" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" bold="true" foreground="[0,51,0]" encoding="UTF-8">3. Um exemplo de uma experi\303\252ncia 'real'.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" foreground="[0,51,0]" encoding="UTF-8">Em um livro, notamos o n\303\272mero de ocorr\303\252ncias de vogais por p\303\241gina e descobrimos que havia 30%.
O universo est\303\241 aqui logicamente o todo </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> , o\303\271 V = &quot;conjunto de vogais &quot;e C =&quot; conjunto de consoantes &quot;: definimos </Font></Text-field>
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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" foreground="[0,51,0]" encoding="UTF-8">On ouvre une page et on choisit une lettre au hasard : on s'int\303\251resse \303\240 l'\303\251v\303\250nement </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiQ0YnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiQ0YnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]"> = &quot;obtenir une consonne&quot;. On a</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal">1. Para todos eventos <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn</Equation> e <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiQkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiQkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn</Equation> temos</Text-field>
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<Input><Text-field style="Text" size="10" layout="Normal"><Font size="12" encoding="UTF-8">Existe equiprobabilidade quando todas as probabilidades elementares s\303\243o iguais, portanto, quando  </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="12">  para todo </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEnJiM5Njk7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSomRWxlbWVudDtGJ0YyRjQvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZLLUYsNiZRJyYjOTM3O0YnRi9GMkY0RjJGNA==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEnJiM5Njk7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSomRWxlbWVudDtGJ0YyRjQvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZLLUYsNiZRJyYjOTM3O0YnRi9GMkY0RjJGNA==</Equation><Font size="12"> . Assim</Font></Text-field>
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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" foreground="[0,51,0]" encoding="UTF-8">Trocamos as letras da palavra &quot;BANC&quot;.
Universo \316\251 \303\251 o conjunto de permuta\303\247\303\265es da palavra, ent\303\243o </Font><Equation executable="false" style="Text" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkobWZlbmNlZEdGJDYoLUYjNiktSSNtaUdGJDYoUScmIzkzNztGJy8lJXNpemVHUSMxMEYnLyUnaXRhbGljR1EmZmFsc2VGJy8lK2ZvcmVncm91bmRHUSlbMCw1MSwwXUYnLyU2c2VsZWN0aW9uLXBsYWNlaG9sZGVyR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Y0L0Y4Rj9GOi8lLHBsYWNlaG9sZGVyR0Y/Rj0vRkFRJ2l0YWxpY0YnRjRGOkZALyUlb3BlbkdRJiZtaWQ7RicvJSZjbG9zZUdGSi1JI21vR0YkNjBRIj1GJ0Y0RjpGPUZALyUmZmVuY2VHRjkvJSpzZXBhcmF0b3JHRjkvJSlzdHJldGNoeUdGOS8lKnN5bW1ldHJpY0dGOS8lKGxhcmdlb3BHRjkvJS5tb3ZhYmxlbGltaXRzR0Y5LyUnYWNjZW50R0Y5LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGW28tSSNtbkdGJDYnUSI0RidGNEY6Rj1GQC1GTjYwUSIhRidGNEY6Rj1GQEZRRlNGVUZXRllGZW5GZ24vRmpuUSwwLjExMTExMTFlbUYnL0Zdb0Zmb0Y0RjpGQA==">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</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> : estamos claramente em uma situa\303\247\303\243o de equiprobabilidade.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" foreground="[0,51,0]" encoding="UTF-8">Este \303\251 o evento elementar</Font><Equation executable="false" style="2D Math" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2KFEiQUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNjBRIj1GJ0YvRjVGOC9GPFEnbm9ybWFsRicvJSZmZW5jZUdGOi8lKnNlcGFyYXRvckdGOi8lKXN0cmV0Y2h5R0Y6LyUqc3ltbWV0cmljR0Y6LyUobGFyZ2VvcEdGOi8lLm1vdmFibGVsaW1pdHNHRjovJSdhY2NlbnRHRjovJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZULUYjNigtRiw2I1EhRictSShtZmVuY2VkR0YkNiktRiM2Ki1GLDYoUSVOQkNBRidGLy9GM0Y6RjVGOEZCRi9GMkY1RjgvJSxwbGFjZWhvbGRlckdGNC8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdGNEY7Ri9GNUY4RkIvJSVvcGVuR1EpJmxicmFjZTtGJy8lJmNsb3NlR1EpJnJicmFjZTtGJ0YvRjVGOEZCRllGL0Y1RjhGQg==</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> ent\303\243o</Font></Text-field>
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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" foreground="[0,51,0]" encoding="UTF-8">Resta fazer uma permuta\303\247\303\243o das letras &quot;B&quot;, &quot;N&quot;, &quot;C&quot;: </Font><Equation executable="false" style="Text" input-equation="" display="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">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</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> ent\303\243o</Font></Text-field>
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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" foreground="[0,51,0]" encoding="UTF-8">Esse resultado deve fazer voc\303\252 pensar ... e pensar na seguinte solu\303\247\303\243o.
Mudamos o universo e escolhemos o todo  </Font><Equation executable="false" style="2D Math" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYtLUkjbWlHRiQ2KFEnJiM5Mzc7RicvJSVzaXplR1EjMTBGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHRjQvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2MFEifkYnRi9GNUY4RjovJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZRLUY+NjBRIidGJ0YvRjVGOEY6RkFGQ0ZFRkdGSUZLRk0vRlBRLDAuMTExMTExMWVtRidGUkY9LUY+NjBRIj1GJ0YvRjVGOEY6RkFGQ0ZFRkdGSUZLRk0vRlBRLDAuMjc3Nzc3OGVtRicvRlNGZ24tRiM2KC1GLDYjUSFGJy1JKG1mZW5jZWRHRiQ2KS1GIzYwLUYsNihRIkJGJ0YvL0YzUSV0cnVlRidGNUY4L0Y7USdpdGFsaWNGJy1GPjYwUSIsRidGL0Y1RjhGOkZBL0ZERmdvRkVGR0ZJRktGTUZPL0ZTUSwwLjMzMzMzMzNlbUYnLUYsNihRIkFGJ0YvRmZvRjVGOEZob0Zqby1GLDYoUSJORidGL0Zmb0Y1RjhGaG9Gam8tRiw2KFEiQ0YnRi9GZm9GNUY4RmhvRi9GZm9GNUY4LyUscGxhY2Vob2xkZXJHRmdvLyU2c2VsZWN0aW9uLXBsYWNlaG9sZGVyR0Znb0Zob0YvRjVGOEY6LyUlb3BlbkdRKSZsYnJhY2U7RicvJSZjbG9zZUdRKSZyYnJhY2U7RidGL0Y1RjhGOkZbb0YvRjVGOEY6</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8">, ent\303\243o </Font><Equation executable="false" style="Text" input-equation="" display="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">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</Equation><Font size="10" foreground="[0,51,0]">. Nesse novo universo, o evento </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiQkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiQkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]"> torna-se o evento </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> e a equiprobabilidade d\303\241 </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2KlEjcHJGJy8lJXNpemVHUSMxMEYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHRjcvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRj8tSShtZmVuY2VkR0YkNictRiM2KS1GLDYoUSJCRidGLy9GNkY0RjhGOy9GPlEnaXRhbGljRictSSNtb0dGJDYwUSJ+RidGL0Y4RjsvRj5RJ25vcm1hbEYnLyUmZmVuY2VHRjcvJSpzZXBhcmF0b3JHRjcvJSlzdHJldGNoeUdGNy8lKnN5bW1ldHJpY0dGNy8lKGxhcmdlb3BHRjcvJS5tb3ZhYmxlbGltaXRzR0Y3LyUnYWNjZW50R0Y3LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGXW8tRk42MFEiJ0YnRi9GOEY7RlFGU0ZVRldGWUZlbkZnbkZpbi9GXG9RLDAuMTExMTExMWVtRidGXm9GL0Y4RjtGUUYvRjhGO0ZRLUZONjBRIj1GJ0YvRjhGO0ZRRlNGVUZXRllGZW5GZ25GaW4vRlxvUSwwLjI3Nzc3NzhlbUYnL0Zfb0Zpby1JJm1mcmFjR0YkNiktSSNtbkdGJDYnUSIxRidGL0Y4RjtGUS1GIzYoLUZfcDYnUSI0RidGL0Y4RjtGUUYvRkpGOEY7RksvJS5saW5ldGhpY2tuZXNzR0ZhcC8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZbcS8lKWJldmVsbGVkR0Y3RjhGL0Y4RjtGUQ==">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</Equation><Font size="10" foreground="[0,51,0]">.</Font></Text-field>
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<Input><Text-field style="Text" bold="true" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" bold="true" foreground="[0,51,0]">2. Desenhar </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2KlEiT0YnLyUlc2l6ZUdRIzEwRicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lK2ZvcmVncm91bmRHUSlbMCw1MSwwXUYnLyUrZXhlY3V0YWJsZUdGNy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGP0YvRjJGOEY7Rj1GQA==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2KlEiT0YnLyUlc2l6ZUdRIzEwRicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lK2ZvcmVncm91bmRHUSlbMCw1MSwwXUYnLyUrZXhlY3V0YWJsZUdGNy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGP0YvRjJGOEY7Rj1GQA==</Equation><Font size="10" bold="true" foreground="[0,51,0]"> / </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" bold="true" foreground="[0,51,0]"> .</Font></Text-field>
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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" bold="true" foreground="[0,51,0]">(i)</Font><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> Uma urna cont\303\251m 3 bolas vermelhas e 2 bolas brancas: uma sacada sucessivamente 3 bolas sem substitui\303\247\303\243o e uma interessada na sequ\303\252ncia formada pelas 3 bolas.
Universo \316\251 \303\251 o conjunto de seq\303\274\303\252ncias sem repeti\303\247\303\243o de 3 elementos entre </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> , ent\303\243o </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> : estamos claramente em uma situa\303\247\303\243o de equiprobabilidade.

Estamos interessados \342\200\213\342\200\213no evento</Font><Font size="10" foreground="[0,51,0]">  </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2KFEiQUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNjBRIj1GJ0YvRjVGOC9GPFEnbm9ybWFsRicvJSZmZW5jZUdGOi8lKnNlcGFyYXRvckdGOi8lKXN0cmV0Y2h5R0Y6LyUqc3ltbWV0cmljR0Y6LyUobGFyZ2VvcEdGOi8lLm1vdmFibGVsaW1pdHNHRjovJSdhY2NlbnRHRjovJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZURi9GNUY4RkI=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2KFEiQUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNjBRIj1GJ0YvRjVGOC9GPFEnbm9ybWFsRicvJSZmZW5jZUdGOi8lKnNlcGFyYXRvckdGOi8lKXN0cmV0Y2h5R0Y6LyUqc3ltbWV0cmljR0Y6LyUobGFyZ2VvcEdGOi8lLm1vdmFibGVsaW1pdHNHRjovJSdhY2NlbnRHRjovJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZURi9GNUY4RkI=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8">&quot; a continua\303\247\303\243o cont\303\251m pelo menos uma bola branca &quot;.
Vamos para complementar: </Font><Equation executable="false" style="2D Math" input-equation="" 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size="10" foreground="[0,51,0]" encoding="UTF-8"> \303\251 o conjunto de su\303\255tes com apenas bolas vermelhas, ent\303\243o  </Font><Equation executable="false" style="Text" input-equation="" 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O resultado foi previs\303\255vel, embora com um pouco de racioc\303\255nio: todas as partes com 2 elementos sendo igualmente prov\303\241veis, basta calcular a probabilidade de que, para uma determinada parte </Font><Equation executable="false" style="Text" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictSShtZmVuY2VkR0YkNigtRiM2LC1JI21uR0YkNiZRIjFGJy8lJXNpemVHUSMxMEYnLyUrZm9yZWdyb3VuZEdRKVswLDUxLDBdRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2L1EifkYnRjhGO0Y+LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZHLyUpc3RyZXRjaHlHRkcvJSpzeW1tZXRyaWNHRkcvJShsYXJnZW9wR0ZHLyUubW92YWJsZWxpbWl0c0dGRy8lJ2FjY2VudEdGRy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlYtRkI2L1EiLEYnRjhGO0Y+RkUvRklRJXRydWVGJ0ZKRkxGTkZQRlJGVC9GWFEsMC4zMzMzMzMzZW1GJy1GNTYmUSIyRidGOEY7Rj5GOC8lJ2l0YWxpY0dGZ25GOy8lLHBsYWNlaG9sZGVyR0Znbi8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdGZ24vRj9RJ2l0YWxpY0YnRjhGO0Y+LyUlb3BlbkdRKSZsYnJhY2U7RicvJSZjbG9zZUdRKSZyYnJhY2U7RidGOEY7Rj4=">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</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8">,a sequ\303\252ncia formada a partir dos elementos desta parte est\303\241 aumentando estritamente; pois s\303\263 podemos formar as duas su\303\255tes </Font><Equation executable="false" style="Text" input-equation="" display="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">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</Equation><Font size="10" foreground="[0,51,0]"> e </Font><Equation executable="false" style="Text" input-equation="" display="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">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</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8">a probabilidade \303\251 </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkmbWZyYWNHRiQ2KS1JI21uR0YkNidRIjFGJy8lJXNpemVHUSMxMEYnLyUrZm9yZWdyb3VuZEdRKVswLDUxLDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2KS1GLzYnUSIyRidGMkY1RjhGOy1JI21vR0YkNjBRIiFGJ0YyRjVGOEY7LyUmZmVuY2VHRjovJSpzZXBhcmF0b3JHRjovJSlzdHJldGNoeUdGOi8lKnN5bW1ldHJpY0dGOi8lKGxhcmdlb3BHRjovJS5tb3ZhYmxlbGltaXRzR0Y6LyUnYWNjZW50R0Y6LyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdGV0YyLyUnaXRhbGljR1EldHJ1ZUYnRjVGOC9GPFEnaXRhbGljRicvJS5saW5ldGhpY2tuZXNzR0YxLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRl1vLyUpYmV2ZWxsZWRHRjpGNUY1RjhGOw==">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</Equation><Font size="10" foreground="[0,51,0]">.</Font></Text-field>
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<Input><Text-field style="Text" bold="true" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" bold="true" foreground="[0,51,0]">3. Desenhar </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" bold="true" foreground="[0,51,0]"> / </Font><Equation executable="false" style="Text" input-equation="" display="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">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</Equation><Font size="10" bold="false" foreground="[0,51,0]"> .</Font></Text-field>
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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" foreground="[0,51,0]" encoding="UTF-8">Uma urna cont\303\251m 5 fichas numeradas de 1 a 5: n\303\263s desenhamos 3 sucessivamente sem substitui\303\247\303\243o e estamos interessados \342\200\213\342\200\213na parte formada pelos 3 n\303\272meros.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" bold="true" foreground="[0,51,0]">(ii)</Font><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> N\303\263s notamos </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiQkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiQkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> o evento &quot;o jogo cont\303\251m apenas um n\302\260 para &quot; .</Font></Text-field>
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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" foreground="[0,51,0]" encoding="UTF-8">Primeiro escolhemos o n\303\272mero par, ent\303\243o </Font><Equation executable="false" style="Text" input-equation="" display="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">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</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> possibilidades; ent\303\243o escolhemos os n\303\272meros \303\255mpares, ent\303\243o </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> possibilidades: ent\303\243o </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" foreground="[0,51,0]"> e</Font></Text-field>
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<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 4" underline="true" bold="true" foreground="[102,102,153]" italic="false" size="10" layout="Heading 4"><Font size="10" underline="true" bold="true" foreground="[102,102,153]" encoding="UTF-8" italic="false">Gr\303\241fico interativo: veja os exemplos anteriores</Font></Text-field></Title><Presentation-Block>
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<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"><Font size="10" bold="true" foreground="[102,102,153]" encoding="UTF-8" italic="true">Escolha a pergunta desejada clicando no bot\303\243o de op\303\247\303\243o ad_hoc. A probabilidade \303\251 dada na forma 'probabilidade te\303\263rica = probabilidade calculada'.
Nota: voc\303\252 pode modificar a totalidade ou parte dos dados abaixo, sujeito \303\240 consist\303\252ncia nas escolhas e valores razo\303\241veis.
Em particular, certos eventos imposs\303\255veis n\303\243o s\303\243o levados em considera\303\247\303\243o: a probabilidade te\303\263rica e / ou a probabilidade calculada (= 0) podem ser falsas.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal" alignment="centred"><EC-RadioButton id="eqRAB1i" caption="1. (i)" groupname="eqRAB" fontcolor="[0,0,0]" fillcolor="[255,255,255]" enabled="true" visible="true" selected="false"><MapleCode action="click-event-handler">use DocumentTools in 

T0 := &quot;i&quot;:
TITRE := EQperm_P: 
PAR := EQperm_E[T0]:

mot := GetProperty(eqTAR1i_1,'value'):
mot := StringTools[Explode](mot):
n0 := nops(mot):

Up := repeat(n0,1):
Us := mot:
U0 := [Up,Us]:

ana := GetProperty(eqTAR1i_2,'value'):
Ed := StringTools[Explode](ana):
Er := PAR[4][2]:
Eb := PAR[4][3]:
E0 := [Ed,Er,Eb]:

PAR := [n0,n0,U0,E0]:
FILM := TITRE(PAR,T0):

eqC1i := FILM[&quot;c&quot;]:
eqG1i := FILM[&quot;g&quot;]:
Do(%eqPLS1 = eqG1i):
  
end use; 
</MapleCode></EC-RadioButton></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L211715" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"><Font size="10" foreground="[102,102,153]">mot = <EC-TextArea id="eqTAR1i_1" enabled="true" visible="true" visiblecharacterwidth="10" visiblerows="1" fontcolor="[0,0,0]" fillcolor="[255,255,255]" contents="BANC" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L215570" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L211815" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal" alignment="centred"><Font size="10" foreground="[102,102,153]">Evento = &quot;anagrama <EC-TextArea id="eqTAR1i_2" enabled="true" visible="true" visiblecharacterwidth="10" visiblerows="1" fontcolor="[0,0,0]" fillcolor="[255,255,255]" contents="NBCA" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea>&quot;</Font></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell padding="5" visible="true" fillcolor="[255,255,255]" rowspan="7" backgroundstyle="0" columnspan="1"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L211704" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="9" layout="Normal" alignment="centred"><EC-Plot id="eqPLS1" visible="true" pixel-width="600" pixel-height="600" continuous="false" delay="100" fillcolor="[255,255,255]" clickx="1.2926956571861519" clicky="-3.1835900379673845" hoverx="-0.9418803418803419" hovery="-0.6615384615384615" startx="1.2926956571861519" starty="-3.1835900379673845" endx="0.9760566705610385" endy="-0.5995749658754628" clickdefault="true" labelreference="L105141" drawcaption="false" captionposition="1" captionalignment="0" show-border="true"><MapleCode action="drag-event-handler">use DocumentTools in 
end use; 
</MapleCode><MapleCode action="click-event-handler">use DocumentTools in 

boo1i  := parse(GetProperty(eqRAB1i,'value')):
boo1ii := parse(GetProperty(eqRAB1ii,'value')):
boo2i  := parse(GetProperty(eqRAB2i,'value')):
boo2ii := parse(GetProperty(eqRAB2ii,'value')):
boo3i  := parse(GetProperty(eqRAB3i,'value')):
boo3ii := parse(GetProperty(eqRAB3ii,'value')):
if       boo1i  then G0 := eqG1i:  C0 := eqC1i:
 else if boo1ii then G0 := eqG1ii: C0 := eqC1ii:
 else if boo2i  then G0 := eqG2i:  C0 := eqC2i:
 else if boo2ii then G0 := eqG2ii: C0 := eqC2ii:
 else if boo3i  then G0 := eqG3i:  C0 := eqC3i:
 else if boo3ii then G0 := eqG3ii: C0 := eqC3ii:
 end if end if end if end if end if end if:

B0 := C0[1]: UU := C0[2]: EE := C0[3]:
r0 := rand(1..nops(EE)):
V0 := [EE[r0()][1]]:
c0 := 2:
Do(%eqPLS1 = HighLight(G0,V0,B0,o0,HL[c0],OPT)):
  
end use; 
</MapleCode><MapleCode action="drag-end-event-handler">use DocumentTools in 
end use; 
</MapleCode><Plot height="-1.0" type="two-dimensional" width="-1.0" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false">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Ig==</Plot></EC-Plot><Font size="9" foreground="[0,0,0]"> </Font></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell padding="5" visible="true" fillcolor="[255,255,255]" rowspan="1" backgroundstyle="0" columnspan="1"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L211879" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal" alignment="centred"><EC-RadioButton id="eqRAB1ii" caption="1. (ii)" groupname="eqRAB" fontcolor="[0,0,0]" fillcolor="[255,255,255]" enabled="true" visible="true" selected="false"><MapleCode action="click-event-handler">use DocumentTools in 

T0 := &quot;ii&quot;:
TITRE := EQperm_P: 
PAR := EQperm_E[T0]:

mot := GetProperty(eqTAR1ii_1,'value'):
mot := StringTools[Explode](mot):
n0 := nops(mot):

Up := repeat(n0,1):
Us := mot:
U0 := [Up,Us]:

img := GetProperty(eqTAR1ii_2,'value'):
Ed := [{mot[1]},{img}]:
Er := PAR[4][2]:
Eb := PAR[4][3]:
E0 := [Ed,Er,Eb]:

PAR := [n0,n0,U0,E0]:
FILM := TITRE(PAR,T0):

eqC1ii := FILM[&quot;c&quot;]:
eqG1ii := FILM[&quot;g&quot;]:
Do(%eqPLS1 = eqG1ii):
  
end use; 
</MapleCode></EC-RadioButton></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L211878" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"><Font size="10" foreground="[102,102,153]">mot = <EC-TextArea id="eqTAR1ii_1" enabled="true" visible="true" visiblecharacterwidth="10" visiblerows="1" fontcolor="[0,0,0]" fillcolor="[255,255,255]" contents="BANC" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L215569" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L211880" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal" alignment="centred"><Font size="10" foreground="[102,102,153]" encoding="UTF-8">Event = &quot;anagramas da palavra que come\303\247a com <EC-TextArea id="eqTAR1ii_2" enabled="true" visible="true" visiblecharacterwidth="5" visiblerows="1" fontcolor="[0,0,0]" fillcolor="[255,255,255]" contents="A" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Font><Font size="10" foreground="[102,102,153]">&quot;</Font></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell padding="5" visible="true" fillcolor="[255,255,255]" rowspan="1" backgroundstyle="0" columnspan="1"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L211822" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal" alignment="centred"><EC-RadioButton id="eqRAB2i" caption="2. (i)" groupname="eqRAB" fontcolor="[0,0,0]" fillcolor="[255,255,255]" enabled="true" visible="true" selected="false"><MapleCode action="click-event-handler">use DocumentTools in 

T0 := &quot;i&quot;:
TITRE := EQarr_P: 
PAR := EQarr_E[T0]:
p0 := parse(GetProperty(eqTAR2i_1,'value')):

n1n2 := parse(GetProperty(eqTAR2i_2,'value')):
n0 := n1n2[1]+n1n2[2]:

Up := n1n2:
Us := [seq('R'[k0],k0=1..n1n2[1]),seq('B'[k0],k0=1..n1n2[2])]:
U0 := [Up,Us]:

Ed := [{seq(k0,k0=1..p0)},{seq('R'[k0],k0=1..n1n2[1])}]:
Er := PAR[4][2]:
Eb := PAR[4][3]:
E0 := [Ed,Er,Eb]:

PAR := [p0,n0,U0,E0]:
FILM := TITRE(PAR,T0):

eqC2i := FILM[&quot;c&quot;]:
eqG2i := FILM[&quot;g&quot;]:
Do(%eqPLS1 = eqG2i):
  
end use; 
</MapleCode></EC-RadioButton></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L215560" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"><Font size="10" foreground="[102,102,153]" encoding="UTF-8">N\303\272mero de sorteios sem desconto =      <EC-TextArea id="eqTAR2i_1" enabled="true" visible="true" visiblecharacterwidth="5" visiblerows="1" fontcolor="[0,0,0]" fillcolor="[255,255,255]" contents="3" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L211821" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"><Font size="10" foreground="[102,102,153]">[bolas vermelhas, bolas brancas]= <EC-TextArea id="eqTAR2i_2" enabled="true" visible="true" visiblecharacterwidth="10" visiblerows="1" fontcolor="[0,0,0]" fillcolor="[255,255,255]" contents="[3, 2]" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L215568" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L211858" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal" alignment="centred"><Font size="10" foreground="[102,102,153]" encoding="UTF-8">Evento = &quot;a continua\303\247\303\243o cont\303\251m apenas bolas vermelhas&quot;</Font></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell padding="5" visible="true" fillcolor="[255,255,255]" rowspan="1" backgroundstyle="0" columnspan="1"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L211832" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal" alignment="centred"><EC-RadioButton id="eqRAB2ii" caption="2. (ii)" groupname="eqRAB" fontcolor="[0,0,0]" fillcolor="[255,255,255]" enabled="true" visible="true" selected="false"><MapleCode action="click-event-handler">use DocumentTools in 

T0 := &quot;ii&quot;:
TITRE := EQarr_P: 
PAR := EQarr_E[T0]:

p0 := parse(GetProperty(eqTAR2ii_1,'value')):

numero := parse(GetProperty(eqTAR2ii_2,'value')):
n0 := nops(numero):

Up := repeat(n0,1):
Us := numero:
U0 := [Up,Us]:

Ed := [{},{}]:
Er := PAR[4][2]:
Eb := PAR[4][3]:
E0 := [Ed,Er,Eb]:

PAR := [p0,n0,U0,E0]:
FILM := TITRE(PAR,T0):

eqC2ii := FILM[&quot;c&quot;]:
eqG2ii := FILM[&quot;g&quot;]:
Do(%eqPLS1 = eqG2ii):
  
end use; 

</MapleCode></EC-RadioButton></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L215562" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"><Font size="10" foreground="[102,102,153]" encoding="UTF-8">N\303\272mero de sorteios sem desconto = <EC-TextArea id="eqTAR2ii_1" enabled="true" visible="true" visiblecharacterwidth="5" visiblerows="1" fontcolor="[0,0,0]" fillcolor="[255,255,255]" contents="2" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L211833" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"><Font size="10" foreground="[102,102,153]" encoding="UTF-8">Num\303\251ros</Font><Font size="10" foreground="[102,102,153]"> =                                    <EC-TextArea id="eqTAR2ii_2" enabled="true" visible="true" visiblecharacterwidth="15" visiblerows="1" fontcolor="[0,0,0]" fillcolor="[255,255,255]" contents="[1, 2, 3]" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L211834" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L211859" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal" alignment="centred"><Font size="10" foreground="[102,102,153]" encoding="UTF-8">Event = &quot;o segundo n\303\272mero \303\251 estritamente maior que o primeiro&quot;</Font></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell padding="5" visible="true" fillcolor="[255,255,255]" rowspan="1" backgroundstyle="0" columnspan="1"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L211842" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal" alignment="centred"><EC-RadioButton id="eqRAB3i" caption="3. (i)" groupname="eqRAB" fontcolor="[0,0,0]" fillcolor="[255,255,255]" enabled="true" visible="true" selected="false"><MapleCode action="click-event-handler">use DocumentTools in 

T0 := &quot;i&quot;:
TITRE := EQcomb_P: 
PAR := EQcomb_E[T0]:

p0 := parse(GetProperty(eqTAR3i_1,'value')):

jeton := parse(GetProperty(eqTAR3i_2,'value')):
n0 := nops(jeton):

Up := repeat(n0,1):
Us := jeton:
U0 := [Up,Us]:

Ed := parse(GetProperty(eqTAR3i_3,'value')):
Er := PAR[4][2]:
Eb := PAR[4][3]:
E0 := [Ed,Er,Eb]:

PAR := [p0,n0,U0,E0]:
FILM := TITRE(PAR,T0):

eqC3i := FILM[&quot;c&quot;]:
eqG3i := FILM[&quot;g&quot;]:
Do(%eqPLS1 = eqG3i):
  
end use; 
</MapleCode></EC-RadioButton></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L215564" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"><Font size="10" foreground="[102,102,153]" encoding="UTF-8">N\303\272mero de sorteios sem desconto = <EC-TextArea id="eqTAR3i_1" enabled="true" visible="true" visiblecharacterwidth="5" visiblerows="1" fontcolor="[0,0,0]" fillcolor="[255,255,255]" contents="3" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L211844" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"><Font size="10" foreground="[102,102,153]">Tokens =                                   <EC-TextArea id="eqTAR3i_2" enabled="true" visible="true" visiblecharacterwidth="15" visiblerows="1" fontcolor="[0,0,0]" fillcolor="[255,255,255]" contents="{1, 2, 3, 4, 5}" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L211843" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L211846" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal" alignment="centred"><Font size="10" foreground="[102,102,153]" encoding="UTF-8">Evento = &quot;o jogo cont\303\251m o n\303\272mero <EC-TextArea id="eqTAR3i_3" enabled="true" visible="true" visiblecharacterwidth="5" visiblerows="1" fontcolor="[0,0,0]" fillcolor="[255,255,255]" contents="3" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Font><Font size="10" foreground="[102,102,153]">&quot;</Font></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell padding="5" visible="true" fillcolor="[255,255,255]" rowspan="1" backgroundstyle="0" columnspan="1"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L211856" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal" alignment="centred"><EC-RadioButton id="eqRAB3ii" caption="3. (ii)" groupname="eqRAB" fontcolor="[0,0,0]" fillcolor="[255,255,255]" enabled="true" visible="true" selected="false"><MapleCode action="click-event-handler">use DocumentTools in 

T0 := &quot;ii&quot;:
TITRE := EQcomb_P: 
PAR := EQcomb_E[T0]:

p0 := parse(GetProperty(eqTAR3ii_1,'value')):

jeton := parse(GetProperty(eqTAR3ii_2,'value')):
n0 := nops(jeton):

Up := repeat(n0,1):
Us := jeton:
U0 := [Up,Us]:

Ed := TypeList(Us,`even`):
Er := PAR[4][2]:
Eb := PAR[4][3]:
E0 := [Ed,Er,Eb]:

PAR := [p0,n0,U0,E0]:
FILM := TITRE(PAR,T0):

eqC3ii := FILM[&quot;c&quot;]:
eqG3ii := FILM[&quot;g&quot;]:
Do(%eqPLS1 = eqG3ii):
  
end use; 
</MapleCode></EC-RadioButton></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L215566" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"><Font size="10" foreground="[102,102,153]" encoding="UTF-8">N\303\272mero de sorteios sem desconto = <EC-TextArea id="eqTAR3ii_1" enabled="true" visible="true" visiblecharacterwidth="5" visiblerows="1" fontcolor="[0,0,0]" fillcolor="[255,255,255]" contents="3" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L211854" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"><Font size="10" foreground="[102,102,153]">Jetons =                                        <EC-TextArea id="eqTAR3ii_2" enabled="true" visible="true" visiblecharacterwidth="15" visiblerows="1" fontcolor="[0,0,0]" fillcolor="[255,255,255]" contents="{1, 2, 3, 4, 5}" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L211855" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L211853" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal" alignment="centred"><Font size="10" foreground="[102,102,153]" encoding="UTF-8">Event = &quot;o jogo cont\303\251m apenas um n\303\272mero par&quot;</Font></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell padding="5" visible="true" fillcolor="[255,255,255]" rowspan="1" backgroundstyle="0" columnspan="1"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L211712" drawlabel="true">
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Do(%eqPLS1 = EP2D):
eqC1i  := []:
eqC1ii := []:
eqC2i  := []:
eqC2ii := []:
eqC3i  := []:
eqC3ii := []:
  
end use; 
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Se </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiQUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiQUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]"> e </Font><Equation executable="false" style="2D Math" input-equation="" 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display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiQUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiQUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]"> e </Font><Equation executable="false" style="2D Math" input-equation="" 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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" foreground="[0,51,0]" encoding="UTF-8">A independ\303\252ncia total implica independ\303\252ncia dois a dois, mas o inverso \303\251 falso.
3. A independ\303\252ncia pode ser previs\303\255vel e permitida em v\303\241rias situa\303\247\303\265es padr\303\243o:
- lan\303\247amento </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KFEicEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0Y1RjgvRjxRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KFEicEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0Y1RjgvRjxRJ25vcm1hbEYn</Equation><Font size="10" foreground="[0,51,0]"> tempos de um dado para </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KFEibkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0Y1RjgvRjxRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KFEibkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0Y1RjgvRjxRJ25vcm1hbEYn</Equation><Font size="10" foreground="[0,51,0]"> rostos distintos
- sorteio ordenado com desconto </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KFEicEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0Y1RjgvRjxRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KFEicEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0Y1RjgvRjxRJ25vcm1hbEYn</Equation><Font size="10" foreground="[0,51,0]"> vezes em uma urna contendo </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KFEibkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0Y1RjgvRjxRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KFEibkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0Y1RjgvRjxRJ25vcm1hbEYn</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> bolas separadas
- distribui\303\247\303\265es de </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KFEicEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0Y1RjgvRjxRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KFEicEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0Y1RjgvRjxRJ25vcm1hbEYn</Equation><Font size="10" foreground="[0,51,0]"> elementos distintos </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KFEibkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0Y1RjgvRjxRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KFEibkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0Y1RjgvRjxRJ25vcm1hbEYn</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> urnas separadas.
Todas essas situa\303\247\303\265es correspondem ao modelo matem\303\241tico de aplica\303\247\303\265es </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KFEicEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0Y1RjgvRjxRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KFEicEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0Y1RjgvRjxRJ25vcm1hbEYn</Equation><Font size="10" foreground="[0,51,0]"> no </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KFEibkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0Y1RjgvRjxRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KFEibkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0Y1RjgvRjxRJ25vcm1hbEYn</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> , ou mesmo su\303\255tes com repeti\303\247\303\243o </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KFEicEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0Y1RjgvRjxRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KFEicEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0Y1RjgvRjxRJ25vcm1hbEYn</Equation><Font size="10" foreground="[0,51,0]"> entre </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KFEibkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0Y1RjgvRjxRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2KFEibkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0Y1RjgvRjxRJ25vcm1hbEYn</Equation><Font size="10" foreground="[0,51,0]">.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[0,51,0]" layout="Normal"><Font size="10" foreground="[0,51,0]" encoding="UTF-8">Al\303\251m desses casos, a independ\303\252ncia pode ser falsa e, caso contr\303\241rio, deve ser comprovada.</Font></Text-field>
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<Input><Text-field style="Text" bold="true" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" bold="true" foreground="[0,51,0]" encoding="UTF-8">1. Um exemplo de uma experi\303\252ncia 'real'.</Font></Text-field>
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N\303\263s notamos </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiTUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiTUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]">  o evento &quot;doente&quot; e </Font><Equation executable="false" style="2D Math" input-equation="" 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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" foreground="[0,51,0]" encoding="UTF-8">ent\303\243o os eventos </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiVkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiVkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]"> e </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiTUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiTUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> (felizmente) n\303\243o s\303\243o independentes.
Observe, por\303\251m, que o valor  </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" foreground="[0,51,0]"> teria tornado os eventos independentes.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" bold="true" foreground="[0,51,0]">2. Sistema de componentes independentes.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" foreground="[0,51,0]" encoding="UTF-8">Uma part\303\255cula est\303\241 andando \342\204\225\303\227\342\204\225 come\303\247ando </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> : os saltos s\303\243o completamente independentes e o salto tem a probabilidade </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEicEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEicEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]"> ,o salto j tem a probabilidade </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> . 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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" foreground="[0,51,0]" encoding="UTF-8">Uma part\303\255cula caminha \342\204\244 a partir de </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW5HRiQ2J1EiMEYnLyUlc2l6ZUdRIzEwRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0YvRjJGNUY4">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW5HRiQ2J1EiMEYnLyUlc2l6ZUdRIzEwRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0YvRjJGNUY4</Equation><Font size="10" foreground="[0,51,0]"> :<Font encoding="UTF-8"> os saltos s\303\243o completamente independentes e o salto +1 tem a probabilidade </Font></Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEicEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEicEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]"> ,o pulo -1 tem a probabilidade </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> . Estamos interessados \342\200\213\342\200\213em longas caminhadas </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbW5HRiQ2J1EiMkYnLyUlc2l6ZUdRIzEwRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNjBRIn5GJ0YvRjJGNUY4LyUmZmVuY2VHRjcvJSpzZXBhcmF0b3JHRjcvJSlzdHJldGNoeUdGNy8lKnN5bW1ldHJpY0dGNy8lKGxhcmdlb3BHRjcvJS5tb3ZhYmxlbGltaXRzR0Y3LyUnYWNjZW50R0Y3LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTy1JI21pR0YkNihRIm5GJ0YvLyUnaXRhbGljR1EldHJ1ZUYnRjJGNS9GOVEnaXRhbGljRidGL0YyRjVGOA==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbW5HRiQ2J1EiMkYnLyUlc2l6ZUdRIzEwRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNjBRIn5GJ0YvRjJGNUY4LyUmZmVuY2VHRjcvJSpzZXBhcmF0b3JHRjcvJSlzdHJldGNoeUdGNy8lKnN5bW1ldHJpY0dGNy8lKGxhcmdlb3BHRjcvJS5tb3ZhYmxlbGltaXRzR0Y3LyUnYWNjZW50R0Y3LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTy1JI21pR0YkNihRIm5GJ0YvLyUnaXRhbGljR1EldHJ1ZUYnRjJGNS9GOVEnaXRhbGljRidGL0YyRjVGOA==</Equation><Font size="10" foreground="[0,51,0]"> que terminam em </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW5HRiQ2J1EiMEYnLyUlc2l6ZUdRIzEwRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0YvRjJGNUY4">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW5HRiQ2J1EiMEYnLyUlc2l6ZUdRIzEwRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0YvRjJGNUY4</Equation><Font size="10" foreground="[0,51,0]">.</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L174386" drawlabel="true">
<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" foreground="[0,51,0]">Idem 3. pela resposta.</Font></Text-field>
</Input>
</Group></Presentation-Block>
</Section></Table-Cell></Table-Row></Table><Table visible="true" editable="true" exterior="all" pagebreak="cell" showlabel="true" title="" plotalignlists="" hiddenborderdisplay="worksheet" interior="group" postexecute="insert" drawcaption="false" width="1083.4586" captionalignment="0" showinput="true" captionposition="1" id="Table3" alignment="left" randomized="false" labelreference="L173062" showgroup="true" order="row"><Table-Column weight="1441" separator="true"></Table-Column><Table-Row align="top" separator="true"><Table-Cell padding="5" visible="true" fillcolor="[250,250,255]" rowspan="1" backgroundstyle="1" columnspan="1">
<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 4" underline="true" bold="true" foreground="[102,102,153]" italic="false" size="10" layout="Heading 4"><Font size="10" underline="true" bold="true" foreground="[102,102,153]" encoding="UTF-8" italic="false">Gr\303\241fico interativo: veja os exemplos anteriores 2., 3. e 4.</Font></Text-field></Title><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L214553" drawlabel="true">
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L214534" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"><Font size="10" bold="true" foreground="[102,102,153]" encoding="UTF-8" italic="true">Escolha a pergunta desejada clicando no bot\303\243o de op\303\247\303\243o ad_hoc.
Nota: voc\303\252 pode modificar a totalidade ou parte dos dados abaixo, sujeito \303\240 consist\303\252ncia nas escolhas e valores razo\303\241veis.</Font><Font size="10" foreground="[102,102,153]">   </Font></Text-field>
</Input>
</Group></Presentation-Block><Table visible="true" editable="true" exterior="all" pagebreak="cell" showlabel="true" title="" plotalignlists="" hiddenborderdisplay="worksheet" interior="group" postexecute="insert" drawcaption="false" width="1062.406" captionalignment="0" showinput="true" captionposition="1" id="Table4" alignment="left" randomized="false" labelreference="L214533" showgroup="true" order="row"><Table-Column weight="390" separator="true"></Table-Column><Table-Column weight="1023" separator="true"></Table-Column><Table-Row align="top" separator="true"><Table-Cell padding="5" visible="true" fillcolor="[255,255,255]" rowspan="1" backgroundstyle="0" columnspan="1"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L214536" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal" alignment="centred"><EC-RadioButton id="indRAB2i" caption="2. (i)" groupname="indRAB" fontcolor="[0,0,0]" fillcolor="[255,255,255]" enabled="true" visible="true" selected="false"><MapleCode action="click-event-handler">use DocumentTools in 

T0 := &quot;i&quot;:
TITRE := INDepr_P: 
PAR := INDepr_E[T0]:

p0 := parse(GetProperty(indTAR2i_1,'value')):

nn := [seq(2,k0=1..p0)]:

Up := parse(GetProperty(indTAR2i_2,'value')):
Up := [seq([100-Up[k0],Up[k0]],k0=1..p0)]:
Us := [seq(['E'[k0],'E'[k0]^c],k0=1..p0)]:
U0 := [Up,Us]:

Ed := [seq('E'[k0],k0=1..p0)]:
Er := PAR[4][2]:
Eb := PAR[4][3]:
E0 := [Ed,Er,Eb]:

PAR := [p0,nn,U0,E0]:
FILM := TITRE(PAR,T0):

indC2i := FILM[&quot;c&quot;]:
indG2i := FILM[&quot;g&quot;]:
Do(%indPLS1 = indG2i):
  
end use; 
</MapleCode></EC-RadioButton></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L214537" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"><Font size="10" foreground="[102,102,153]" encoding="UTF-8">N\303\272mero de componentes = <EC-TextArea id="indTAR2i_1" enabled="true" visible="true" visiblecharacterwidth="5" visiblerows="1" fontcolor="[0,0,0]" fillcolor="[255,255,255]" contents="3" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L218659" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"><Font size="10" foreground="[102,102,153]">Taxa de falha do componente em% (valores inteiros ) =     </Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L214541" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal" alignment="centred"><Font size="10" foreground="[102,102,153]"> <EC-TextArea id="indTAR2i_2" enabled="true" visible="true" visiblecharacterwidth="15" visiblerows="1" fontcolor="[0,0,0]" fillcolor="[255,255,255]" contents="[30, 10, 20]" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L218655" drawlabel="true">
<Input><Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L214552" drawlabel="true">
<Input><Text-field style="Text" layout="Normal" alignment="centred"><Font size="10" foreground="[102,102,153]" encoding="UTF-8">Event = &quot;o sistema est\303\241 funcionando&quot;</Font></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell padding="5" visible="true" fillcolor="[255,255,255]" rowspan="4" backgroundstyle="0" columnspan="1"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L225208" drawlabel="true">
<Input><Text-field style="Text" layout="Normal" alignment="centred"><EC-Plot id="indPLS1" visible="true" pixel-width="600" pixel-height="600" continuous="false" delay="100" fillcolor="[255,255,255]" clickx="-1.2219034713571861" clicky="-3.9929269053013177" hoverx="1.0307692307692307" hovery="0.3914529914529914" startx="-1.2219034713571861" starty="-3.9929269053013177" endx="0.9760566705610385" endy="-0.5995749658754628" clickdefault="true" labelreference="L226729" drawcaption="false" captionposition="1" captionalignment="0" show-border="true"><MapleCode action="drag-event-handler">use DocumentTools in 
end use; 
</MapleCode><MapleCode action="click-event-handler">use DocumentTools in 

boo2i  := parse(GetProperty(indRAB2i,'value')):
boo2ii := parse(GetProperty(indRAB2ii,'value')):
boo3   := parse(GetProperty(indRAB3,'value')):
if       boo2i  then G0 := indG2i:  C0 := indC2i:
 else if boo2ii then G0 := indG2ii: C0 := indC2ii:
 else if boo3   then G0 := indG3:   C0 := indC3:
 end if end if end if:

if boo3 then OPT1 := copy(OPT): OPT1[&quot;ij&quot;] := [1,1]: OPT1[&quot;mo&quot;] := &quot;P&quot;:
	   else OPT1 := OPT:
	   end if:
B0 := C0[1]: UU := C0[2]: EE := C0[3]:
r0 := rand(1..nops(EE)):
V0 := [EE[r0()][1]]:
c0 := 2:
if boo3 then Do(%indPLS1 = EventWalk(G0,op(V0),B0,o0,HL[c0],OPT1))
	   else Do(%indPLS1 = HighLight(G0,V0,B0,o0,HL[c0],OPT1))
	   end if:
  
end use; 
</MapleCode><MapleCode action="drag-end-event-handler">use DocumentTools in 
end use; 
</MapleCode><Plot height="-1.0" type="two-dimensional" width="-1.0" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false">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Ig==</Plot></EC-Plot> <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell padding="5" visible="true" fillcolor="[255,255,255]" rowspan="1" backgroundstyle="0" columnspan="1"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L214691" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal" alignment="centred"><EC-RadioButton id="indRAB2ii" caption="2. (ii)" groupname="indRAB" fontcolor="[0,0,0]" fillcolor="[255,255,255]" enabled="true" visible="true" selected="false"><MapleCode action="click-event-handler">use DocumentTools in 

T0 := &quot;ii&quot;:
TITRE := INDepr_P: 
PAR := INDepr_E[T0]:

p0 := parse(GetProperty(indTAR2ii_1,'value')):

nn := [seq(2,k0=1..p0)]:

Up := parse(GetProperty(indTAR2ii_2,'value')):
Up := [seq([100-Up[k0],Up[k0]],k0=1..p0)]:
Us := [seq(['E'[k0],'E'[k0]^c],k0=1..p0)]:
U0 := [Up,Us]:

Ed := [seq('E'[k0]^c,k0=1..p0)]:
Er := PAR[4][2]:
Eb := PAR[4][3]:
E0 := [Ed,Er,Eb]:

PAR := [p0,nn,U0,E0]:
FILM := TITRE(PAR,T0):

indC2ii := FILM[&quot;c&quot;]:
indG2ii := FILM[&quot;g&quot;]:
Do(%indPLS1 = indG2ii):
  
end use; 
</MapleCode></EC-RadioButton></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L214692" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"><Font size="10" foreground="[102,102,153]" encoding="UTF-8">N\303\272mero de componentes = <EC-TextArea id="indTAR2ii_1" enabled="true" visible="true" visiblecharacterwidth="5" visiblerows="1" fontcolor="[0,0,0]" fillcolor="[255,255,255]" contents="3" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L214690" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"><Font size="10" foreground="[102,102,153]">Tfalha de componente= <EC-TextArea id="indTAR2ii_2" enabled="true" visible="true" visiblecharacterwidth="15" visiblerows="1" fontcolor="[0,0,0]" fillcolor="[255,255,255]" contents="[30, 10, 20]" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L218656" drawlabel="true">
<Input><Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L214689" drawlabel="true">
<Input><Text-field style="Text" layout="Normal" alignment="centred"><Font size="10" foreground="[102,102,153]" encoding="UTF-8">Event = &quot;o sistema est\303\241 inoperante&quot;</Font></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell padding="5" visible="true" fillcolor="[255,255,255]" rowspan="1" backgroundstyle="0" columnspan="1"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L214544" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal" alignment="centred"><EC-RadioButton id="indRAB3" caption="3. et 4." groupname="indRAB" fontcolor="[0,0,0]" fillcolor="[255,255,255]" enabled="true" visible="true" selected="false"><MapleCode action="click-event-handler">use DocumentTools in 

T0 := &quot;i&quot;:
TITRE := INDwalk_P: 
PAR := INDwalk_E[T0]:

n0 := parse(GetProperty(indTAR3_1,'value')):
p0 := parse(GetProperty(indTAR3_2,'value'))/100:

Up := parse(GetProperty(indTAR3_2,'value')):
Up := [100-Up,Up]:
Us := [&quot;O&quot;,&quot;N&quot;]:
U0 := [Up,Us]:

Ed := [[n0,n0]]:
Er := PAR[4][2]:
Eb := PAR[4][3]:
E0 := [Ed,Er,Eb]:

PAR := [2*n0,'nul',U0,E0]:
FILM := TITRE(PAR,T0):

indC3 := FILM[&quot;c&quot;]:
indG3 := FILM[&quot;g&quot;]:
Do(%indPLS1 = indG3):

pr := binomial(2*n0,n0)*(p0*(1-p0))^n0:
Do(%indTAR3_3 = evalf(pr,3)):
  
end use; 
</MapleCode></EC-RadioButton></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L214540" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"><Font size="10" foreground="[102,102,153]" italic="true">n</Font><Font size="10" foreground="[102,102,153]"> = <EC-TextArea id="indTAR3_1" enabled="true" visible="true" visiblecharacterwidth="5" visiblerows="1" fontcolor="[0,0,0]" fillcolor="[255,255,255]" contents="3" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L214737" drawlabel="true">
<Input><Text-field style="Text" layout="Normal"><Font size="10" foreground="[102,102,153]" italic="true">p</Font><Font size="10" foreground="[102,102,153]"> em % (valores inteiros) = <EC-TextArea id="indTAR3_2" enabled="true" visible="true" visiblecharacterwidth="10" visiblerows="1" fontcolor="[0,0,0]" fillcolor="[255,255,255]" contents="40" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L218657" drawlabel="true">
<Input><Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L214539" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal" alignment="centred"><Font size="10" foreground="[102,102,153]">Evento = &quot;o caminho do comprimento </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" foreground="[102,102,153]"> termina em </Font><Equation executable="false" style="2D Math" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkobWZlbmNlZEdGJDYnLUYjNistSSNtaUdGJDYoUSJuRicvJSVzaXplR1EjMTBGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2ZvcmVncm91bmRHUS5bMTAyLDEwMiwxNTNdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYwUSJ+RidGNEY6Rj0vRkFRJ25vcm1hbEYnLyUmZmVuY2VHRj8vJSpzZXBhcmF0b3JHRj8vJSlzdHJldGNoeUdGPy8lKnN5bW1ldHJpY0dGPy8lKGxhcmdlb3BHRj8vJS5tb3ZhYmxlbGltaXRzR0Y/LyUnYWNjZW50R0Y/LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGWS1GRDYwUSIsRidGNEY6Rj1GR0ZJL0ZMRjlGTUZPRlFGU0ZVRlcvRmVuUSwwLjMzMzMzMzNlbUYnRkNGMEY0RjpGPUZHRjRGOkY9RkdGNEY6Rj1GRw==</Equation><Font size="10" foreground="[102,102,153]">&quot;</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L214699" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal" alignment="centred"><Font size="10" foreground="[102,102,153]">Evento = &quot;o caminho do comprimento </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" foreground="[102,102,153]"> termina em 0&quot;</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L240571" drawlabel="true">
<Input><Text-field style="Text" layout="Normal" alignment="centred"><Font size="10" foreground="[102,102,153]">Probabilidade = <EC-TextArea id="indTAR3_3" enabled="true" visible="true" visiblecharacterwidth="10" visiblerows="1" fontcolor="[0,0,0]" fillcolor="[255,255,255]" contents=".375" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Font></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell padding="5" visible="true" fillcolor="[255,255,255]" rowspan="1" backgroundstyle="0" columnspan="1"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L226731" drawlabel="true">
<Input><Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L226733" drawlabel="true">
<Input><Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L226735" drawlabel="true">
<Input><Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L226737" drawlabel="true">
<Input><Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L226739" drawlabel="true">
<Input><Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L226741" drawlabel="true">
<Input><Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L226743" drawlabel="true">
<Input><Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L226745" drawlabel="true">
<Input><Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L226763" drawlabel="true">
<Input><Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L214711" drawlabel="true">
<Input><Text-field style="Text" layout="Normal" alignment="centred"><EC-RadioButton id="indRAB0" caption="Reset" groupname="indRAB" fontcolor="[0,0,0]" fillcolor="[255,255,255]" enabled="true" visible="true" selected="true"><MapleCode action="click-event-handler">use DocumentTools in 

Do(%indPLS1 = EP2D):
indC1  := []:
indC2i  := []:
indC2ii := []:
indC3  := []:
  
end use; 
</MapleCode></EC-RadioButton></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row></Table>
</Section></Table-Cell></Table-Row></Table><Table visible="true" editable="true" exterior="all" pagebreak="cell" showlabel="true" title="" plotalignlists="" hiddenborderdisplay="worksheet" interior="group" postexecute="insert" drawcaption="false" width="1081.9548" captionalignment="0" showinput="true" captionposition="1" id="Table5" alignment="left" randomized="false" labelreference="L173076" showgroup="true" order="row"><Table-Column weight="809" separator="true"></Table-Column><Table-Column weight="809" separator="true"></Table-Column><Table-Row align="top" separator="true"><Table-Cell padding="5" visible="true" fillcolor="[255,250,250]" rowspan="1" backgroundstyle="1" columnspan="1">
<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field bookmark="td21" style="Heading 3" italic="false" size="10" layout="Heading 3"><Hyperlink linktarget="Wks:#ex21" hyperlink="true"><Font size="12" underline="true" style="Heading 3" foreground="[153,51,102]" italic="false">TD 2.1</Font></Hyperlink></Text-field></Title>
</Section></Table-Cell><Table-Cell padding="5" visible="true" fillcolor="[255,250,250]" rowspan="1" backgroundstyle="1" columnspan="1">
<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 3" foreground="[153,51,102]" italic="false" size="10" layout="Heading 3"><Font size="12" foreground="[192,192,192]" italic="false">WIMS 2.1</Font></Text-field></Title>
</Section></Table-Cell></Table-Row></Table>
</Section>
<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field bookmark="co22" style="Heading 2" size="10" layout="Heading 2"><Font size="14">2.2.  Teste repetido independentemente</Font></Text-field></Title><Table visible="true" editable="true" exterior="all" pagebreak="cell" showlabel="true" title="" plotalignlists="" hiddenborderdisplay="worksheet" interior="group" postexecute="insert" drawcaption="false" drawtitle="false" width="1081.9548" captionalignment="0" showinput="true" captionposition="1" id="Table6" alignment="left" randomized="false" labelreference="L173910" showgroup="true" order="row"><Table-Column weight="1439" separator="true"></Table-Column><Table-Row align="top" separator="true"><Table-Cell padding="5" visible="true" fillcolor="[255,255,240]" rowspan="1" backgroundstyle="1" columnspan="1"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L173948" drawlabel="true">
<Input><Text-field style="Text" foreground="[51,51,51]" layout="Normal"><Font foreground="[51,51,51]">Consideramos um teste original em </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRK1s1MSw1MSw1MV1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YyRjUvRjlRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRK1s1MSw1MSw1MV1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YyRjUvRjlRJ25vcm1hbEYn</Equation><Font foreground="[51,51,51]" encoding="UTF-8"> quest\303\265es e notamos </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font foreground="[51,51,51]">todos os resultados deste evento.</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L173949" drawlabel="true">
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Se fizermos uma suposi\303\247\303\243o de equiprobabilidade em \316\251 ent\303\243o a independ\303\252ncia dos testes \303\251 equivalente \303\240 equiprobabilidade em </Font><Equation executable="false" style="2D Math" input-equation="" 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foreground="[51,51,51]" encoding="UTF-8"> : cada su\303\255te</Font><Equation executable="false" style="2D Math" input-equation="" 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foreground="[51,51,51]" encoding="UTF-8"> a ent\303\243o a mesma probabilidade </Font><Equation executable="false" style="2D Math" input-equation="" 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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" foreground="[0,51,0]">portanto, a equiprobabilidade em </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font size="10" foreground="[0,51,0]"> :e reciprocamente.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" foreground="[0,51,0]" encoding="UTF-8">Podemos descrever um teste repetido por uma \303\241rvore de probabilidade: cada repeti\303\247\303\243o adiciona um grau de profundidade na \303\241rvore.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" foreground="[0,51,0]" encoding="UTF-8">- No k-\303\250me teste corresponde os n\303\263s da \303\241rvore \303\240 profundidade </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEia0YnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEia0YnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> :eles representam os poss\303\255veis resultados durante este </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEia0YnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEia0YnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8">-\303\250mteste.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" foreground="[0,51,0]" encoding="UTF-8">- Os n\303\263s s\303\243o conectados pelos galhos da \303\241rvore: uma s\303\251rie de galhos cont\303\255guos \303\251 chamada de caminho.
- A cada ramo da \303\241rvore \303\251 atribu\303\255do um peso, que \303\251 a probabilidade de transi\303\247\303\243o de um n\303\263 para um n\303\263 vizinho: a probabilidade de um caminho \303\251 o produto das probabilidades dos ramos do caminho.</Font><Font size="10" foreground="[0,51,0]"> </Font></Text-field>
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<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L174051" drawlabel="true">
<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" foreground="[0,51,0]">Nesse universo, o evento </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiQUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiQUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> \303\251 o evento elementar </Font><Equation executable="false" style="Text" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictSShtZmVuY2VkR0YkNigtRiM2KS1GLDYnUSNSUkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGN0Y6Rj0vJSxwbGFjZWhvbGRlckdGPC8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdGPEZARjdGPS9GQVEnbm9ybWFsRicvJSVvcGVuR1EpJmxicmFjZTtGJy8lJmNsb3NlR1EpJnJicmFjZTtGJ0Y3Rj1GRw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictSShtZmVuY2VkR0YkNigtRiM2KS1GLDYnUSNSUkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGN0Y6Rj0vJSxwbGFjZWhvbGRlckdGPC8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdGPEZARjdGPS9GQVEnbm9ybWFsRicvJSVvcGVuR1EpJmxicmFjZTtGJy8lJmNsb3NlR1EpJnJicmFjZTtGJ0Y3Rj1GRw==</Equation><Font size="10" foreground="[0,51,0]"> , de probabilidade </Font><Equation executable="false" style="Text" input-equation="" display="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">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</Equation><Font size="10" foreground="[0,51,0]"> .</Font></Text-field>
</Input>
</Group></Presentation-Block>
</Section></Table-Cell></Table-Row></Table><Table visible="true" editable="true" exterior="all" pagebreak="cell" showlabel="true" title="" plotalignlists="" hiddenborderdisplay="worksheet" interior="group" postexecute="insert" drawcaption="false" width="1083.4586" captionalignment="0" showinput="true" captionposition="1" id="Table3" alignment="left" randomized="false" labelreference="L173378" showgroup="true" order="row"><Table-Column weight="1441" separator="true"></Table-Column><Table-Row align="top" separator="true"><Table-Cell padding="5" visible="true" fillcolor="[250,250,255]" rowspan="1" backgroundstyle="1" columnspan="1">
<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 4" underline="true" bold="true" foreground="[102,102,153]" italic="false" size="10" layout="Heading 4"><Font size="10" underline="true" bold="true" foreground="[102,102,153]" encoding="UTF-8" italic="false">Gr\303\241fico interativo: veja os exemplos anteriores
Escolha a pergunta desejada clicando no bot\303\243o de op\303\247\303\243o ad_hoc.
Nota: voc\303\252 pode modificar a totalidade ou parte dos dados abaixo, sujeito \303\240 consist\303\252ncia nas escolhas e valores razo\303\241veis.</Font></Text-field></Title><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L214609" drawlabel="true">
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L214590" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L214594" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"><Font size="10" foreground="[102,102,153]">  </Font></Text-field>
</Input>
</Group></Presentation-Block><Table visible="true" editable="true" exterior="all" pagebreak="cell" showlabel="true" title="" plotalignlists="" hiddenborderdisplay="worksheet" interior="group" postexecute="insert" drawcaption="false" width="1062.406" captionalignment="0" showinput="true" captionposition="1" id="Table4" alignment="left" randomized="false" labelreference="L214589" showgroup="true" order="row"><Table-Column weight="390" separator="true"></Table-Column><Table-Column weight="1023" separator="true"></Table-Column><Table-Row align="top" separator="true"><Table-Cell padding="5" visible="true" fillcolor="[255,255,255]" rowspan="1" backgroundstyle="0" columnspan="1"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L214625" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal" alignment="centred"><EC-RadioButton id="eprRAB1" caption="1." groupname="eprRAB" fontcolor="[0,0,0]" fillcolor="[255,255,255]" enabled="true" visible="true" selected="false"><MapleCode action="click-event-handler">use DocumentTools in 

T0 := &quot;i&quot;:
TITRE := EPRind_P: 
PAR := EPRind_E[T0]:

p0 := parse(GetProperty(eprTAR1_1,'value')):

n0 := parse(GetProperty(eprTAR1_2,'value')):

Up := repeat(n0,1):
Us := [seq(k,k=1..n0)]:
U0 := [Up,Us]:

Ed := [{},{}]:
Er := PAR[4][2]:
Eb := PAR[4][3]:
E0 := [Ed,Er,Eb]:

PAR := [p0,n0,U0,E0]:
FILM := TITRE(PAR,T0):

eprC1 := FILM[&quot;c&quot;]:
eprG1 := FILM[&quot;g&quot;]:
Do(%eprPLS1 = eprG1):
  
end use; 
</MapleCode></EC-RadioButton></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L217001" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"><Font size="10" foreground="[102,102,153]" encoding="UTF-8">N\303\272mero de arremessos =  <EC-TextArea id="eprTAR1_1" enabled="true" visible="true" visiblecharacterwidth="5" visiblerows="1" fontcolor="[0,0,0]" fillcolor="[255,255,255]" contents="2" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L214624" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"><Font size="10" foreground="[102,102,153]" encoding="UTF-8">N\303\272mero de faces =     <EC-TextArea id="eprTAR1_2" enabled="true" visible="true" visiblecharacterwidth="5" visiblerows="1" fontcolor="[0,0,0]" fillcolor="[255,255,255]" contents="4" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Font></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell padding="5" visible="true" fillcolor="[255,255,255]" rowspan="4" backgroundstyle="0" columnspan="1"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L214591" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="9" layout="Normal" alignment="centred"><EC-Plot id="eprPLS1" visible="true" pixel-width="600" pixel-height="600" continuous="false" delay="100" fillcolor="[255,255,255]" clickx="2.7301264812131647" clicky="0.341026623646429" hoverx="6.797467479613215" hovery="-2.808106892719165" startx="2.7301264812131647" starty="0.341026623646429" endx="0.9760566705610385" endy="-0.5995749658754628" clickdefault="true" labelreference="L105141" drawcaption="false" captionposition="1" captionalignment="0" show-border="true"><MapleCode action="drag-event-handler">use DocumentTools in 
end use; 
</MapleCode><MapleCode action="click-event-handler">use DocumentTools in 

boo1   := parse(GetProperty(eprRAB1,'value')):
boo2i  := parse(GetProperty(eprRAB2i,'value')):
boo2ii := parse(GetProperty(eprRAB2ii,'value')):
if       boo1   then G0 := eprG1:   C0 := eprC1:
 else if boo2i  then G0 := eprG2i:  C0 := eprC2i:
 else if boo2ii then G0 := eprG2ii: C0 := eprC2ii:
 end if end if end if:

B0 := C0[1]: UU := C0[2]: EE := C0[3]:
if parse(boo1) then r0 := rand(1..nops(UU)):
	               V0 := [UU[r0()][1]]:
	               c0 := 1:
	          else r0 := rand(1..nops(EE)):
	               V0 := [EE[r0()][1]]:
	               c0 := 2:
	          end if:
Do(%eprPLS1 = HighLight(G0,V0,B0,o0,HL[c0],OPT)):
  
end use; 
</MapleCode><MapleCode action="drag-end-event-handler">use DocumentTools in 
end use; 
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se6"/%'italicGQ&false6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ*[0,0,139]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'normal6"/%%openGQ"[6"/%&closeGQ"]6"/%'familyGQ0Times~New~Roman6"/%%sizeGQ#126"/%%boldGQ&false6"/%'italicGQ&false6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'normal6"/%'familyGQ0Times~New~Roman6"/%%sizeGQ"96"/%%boldGQ&false6"/%'italicGQ&false6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ*[0,0,139]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'normal6"/%'familyGQ0Times~New~Roman6"/%%sizeGQ#126"/%%boldGQ&false6"/%'italicGQ&false6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'normal6"-I%mrowG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"65-I#msG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"6#Q$~=~6"/%'familyGQ0Times~New~Roman6"/%%sizeGQ"96"/%%boldGQ&false6"/%'italicGQ&false6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ*[0,0,139]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'normal6"-I&mfracG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"6*-I#mnG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"65Q"96"/%'familyGQ0Times~New~Roman6"/%%sizeGQ"96"/%%boldGQ&false6"/%'italicGQ&false6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ*[0,0,139]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'normal6"-I#mnG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"65Q#166"/%'familyGQ0Times~New~Roman6"/%%sizeGQ"96"/%%boldGQ&false6"/%'italicGQ&false6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ*[0,0,139]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'normal6"/%.linethicknessGQ"16"/%+denomalignGQ'center6"/%)numalignGQ'center6"/%)bevelledGQ&false6"/%+foregroundGQ*[0,0,139]6"/%+backgroundGQ.[255,255,255]6"-%&COLORG6&%$RGBG$""!!""$""!!""$")2)4X&!")-%%FONTG6%%&TIMESG%&ROMANG""*-&%&_AXISG6#"""6&-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-&%&_AXISG6#""#6&-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-%*AXESSTYLEG6#%%NONEG-%(SCALINGG6#%.UNCONSTRAINEDG-%)_VISIBLEG6#"""-%%ROOTG6'-%)BOUNDS_XG6#$"$+"!""-%)BOUNDS_YG6#$"$S"!""-%-BOUNDS_WIDTHG6#$"%?b!""-%.BOUNDS_HEIGHTG6#$"%5c!""-%)CHILDRENG6"-%+ANNOTATIONG6'-%)BOUNDS_XG6#$""!!""-%)BOUNDS_YG6#$""!!""-%-BOUNDS_WIDTHG6#$"%+S!""-%.BOUNDS_HEIGHTG6#$"%+S!""-%)CHILDRENG6"Ig==</Plot></EC-Plot><Font size="9" foreground="[0,0,0]"> </Font></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell padding="5" visible="true" fillcolor="[255,255,255]" rowspan="1" backgroundstyle="0" columnspan="1"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L214592" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal" alignment="centred"><EC-RadioButton id="eprRAB2i" caption="2. Par \303\251quiprobabilit\303\251" groupname="eprRAB" fontcolor="[0,0,0]" fillcolor="[255,255,255]" enabled="true" visible="true" selected="false"><MapleCode action="click-event-handler">use DocumentTools in 

T0 := &quot;ii&quot;:
TITRE := EPRind_P: 
PAR := EPRind_E[T0]:

p0 := parse(GetProperty(eprTAR2i_1,'value')):

n1n2 := parse(GetProperty(eprTAR2i_2,'value')):
n0 := n1n2[1]+n1n2[2]:

Up := n1n2:
Us := [seq('R'[k0],k0=1..n1n2[1]),seq('B'[k0],k0=1..n1n2[2])]:
U0 := [Up,Us]:

Ed := [{seq(k0,k0=1..p0)},{seq('R'[k0],k0=1..n1n2[1])}]:
Er := PAR[4][2]:
Eb := PAR[4][3]:
E0 := [Ed,Er,Eb]:

PAR := [p0,n0,U0,E0]:
FILM := TITRE(PAR,T0):

eprC2i := FILM[&quot;c&quot;]:
eprG2i := FILM[&quot;g&quot;]:
Do(%eprPLS1 = eprG2i):
  
end use; 
</MapleCode></EC-RadioButton></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L217004" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"><Font size="10" foreground="[102,102,153]" encoding="UTF-8">N\303\272mero de sorteios com desconto =      <EC-TextArea id="eprTAR2i_1" enabled="true" visible="true" visiblecharacterwidth="5" visiblerows="1" fontcolor="[0,0,0]" fillcolor="[255,255,255]" contents="2" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L214593" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"><Font size="10" foreground="[102,102,153]">[bolas vermelhas, bolas brancas ] = <EC-TextArea id="eprTAR2i_2" enabled="true" visible="true" visiblecharacterwidth="10" visiblerows="1" fontcolor="[0,0,0]" fillcolor="[255,255,255]" contents="[3, 1]" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L214685" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L214608" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal" alignment="centred"><Font size="10" foreground="[102,102,153]" encoding="UTF-8">Evento = &quot;a continua\303\247\303\243o cont\303\251m apenas bolas vermelhas&quot;</Font></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell padding="5" visible="true" fillcolor="[255,255,255]" rowspan="1" backgroundstyle="0" columnspan="1"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L214750" drawlabel="true">
<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal" alignment="centred"><EC-RadioButton id="eprRAB2ii" caption="2. Par ind\303\251pendance" groupname="eprRAB" fontcolor="[0,0,0]" fillcolor="[255,255,255]" enabled="true" visible="true" selected="true"><MapleCode action="click-event-handler">use DocumentTools in 

T0 := &quot;iii&quot;:
TITRE := EPRind_P: 
PAR := EPRind_E[T0]:

p0 := parse(GetProperty(eprTAR2i_1,'value')):

n1n2 := parse(GetProperty(eprTAR2i_2,'value')):
n0 := nops(n1n2):

Up := n1n2:
Us := ['R','B']:
U0 := [Up,Us]:

Ed := [{seq(k0,k0=1..p0)},{'R'}]:
Er := PAR[4][2]:
Eb := PAR[4][3]:
E0 := [Ed,Er,Eb]:

PAR := [p0,n0,U0,E0]:
FILM := TITRE(PAR,T0):

eprC2ii := FILM[&quot;c&quot;]:
eprG2ii := FILM[&quot;g&quot;]:
Do(%eprPLS1 = eprG2ii):
  
end use; 
</MapleCode></EC-RadioButton></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
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<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"><Font size="10" foreground="[102,102,153]" encoding="UTF-8">N\303\272mero de sorteios com desconto =      <EC-TextArea id="eprTAR2ii_1" enabled="true" visible="true" visiblecharacterwidth="5" visiblerows="1" fontcolor="[0,0,0]" fillcolor="[255,255,255]" contents="2" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Font></Text-field>
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<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal"><Font size="10" foreground="[102,102,153]">[bolas vermelhas, bolas brancas] = <EC-TextArea id="eprTAR2ii_2" enabled="true" visible="true" visiblecharacterwidth="10" visiblerows="1" fontcolor="[0,0,0]" fillcolor="[255,255,255]" contents="[3, 1]" editable="true" wrapping="true" show-border="true" password="false"></EC-TextArea></Font></Text-field>
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<Input><Text-field style="Text" foreground="[102,102,153]" size="10" layout="Normal" alignment="centred"><Font size="10" foreground="[102,102,153]" encoding="UTF-8">Evento = &quot;a continua\303\247\303\243o cont\303\251m apenas bolas vermelhas&quot;</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal" alignment="centred"><EC-RadioButton id="eprRAB0" caption="Reset" groupname="eprRAB" fontcolor="[0,0,0]" fillcolor="[255,255,255]" enabled="true" visible="true" selected="false"><MapleCode action="click-event-handler">use DocumentTools in 

Do(%eprPLS1 = EP2D):
eprC1  := []:
eprC2  := []:
  
end use; 
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<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 1" foreground="[153,51,102]" layout="Heading 1" alignment="centred"><Font foreground="[153,51,102]" encoding="UTF-8">Exerc\303\255cios</Font></Text-field></Title>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]" encoding="UTF-8">1. N\303\263s consideramos o universo </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font foreground="[153,51,102]" encoding="UTF-8"> e assumimos que as probabilidades dos elementos de \316\251 s\303\243o proporcionais a estes: ou seja, existe um real \316\261 tal que </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font foreground="[153,51,102]">  para todo </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1Eia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1Eia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]">.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font bold="true" foreground="[153,51,102]">Pr</Font><Font foreground="[153,51,102]" encoding="UTF-8"> do conjunto de elementos pares e do conjunto de elementos \303\255mpares quando </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2L1EiPUYnRjJGNS9GOVEnbm9ybWFsRicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JlEiMkYnRjJGNUY/RjJGNUY/">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2L1EiPUYnRjJGNS9GOVEnbm9ybWFsRicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JlEiMkYnRjJGNUY/RjJGNUY/</Equation><Font foreground="[153,51,102]">.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]" encoding="UTF-8">2. N\303\263s consideramos o universo </Font><Equation executable="false" style="2D Math" input-equation="" 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foreground="[153,51,102]"> : assumimos que os eventos elementares da forma </Font><Equation executable="false" style="2D Math" input-equation="" 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foreground="[153,51,102]" encoding="UTF-8"> tem a probabilidade \316\261 enquanto os outros t\303\252m a probabilidade </Font><Equation executable="false" style="Text" input-equation="" 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Calcule \316\261 ent\303\243o a probabilidade do evento </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font foreground="[153,51,102]">.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]" encoding="UTF-8">Simultaneamente, jogue 3 dados equiprob\303\241veis \342\200\213\342\200\213de 6 lados.
Para que a soma dos d\303\255gitos seja igual a 10.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]">1. Consideramos dois eventos </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font foreground="[153,51,102]"> e damos</Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]" encoding="UTF-8">Trocamos as letras da palavra BABAR.

(i) Pr para obter a mesma palavra.
(ii) Pr que a palavra come\303\247a com B.
(iii) Pr que o A se segue.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal" alignment="right"><Hyperlink linktarget="Wks:#td13" hyperlink="true"><Font style="Hyperlink" foreground="[153,51,102]">Retour</Font></Hyperlink></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]">1. Escolhemos aleatoriamente um aplicativo </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font foreground="[153,51,102]"> . </Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font bold="true" foreground="[153,51,102]">Pr </Font><Font foreground="[153,51,102]">que seja injetivo.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]" encoding="UTF-8">2. Uma sala cont\303\251m 20 pessoas, mas n\303\243o eu.
(i) Pr que duas pessoas nascem no mesmo dia.
(ii) Pr que uma pessoa (pelo menos) nasceu no mesmo dia que eu.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal" alignment="right"><Hyperlink linktarget="Wks:#td13" hyperlink="true"><Font style="Hyperlink" foreground="[153,51,102]">Retour</Font></Hyperlink></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]" encoding="UTF-8">1. Um grupo de 10 pessoas \303\251 composto por 3 homens e 7 mulheres: 5 pessoas s\303\243o escolhidas aleatoriamente.
(i) Pr para escolher 0,1,2,3 homens.
(ii) Pr para escolher pelo menos um homem.

2. Distribua 10 ovos indistingu\303\255veis em 3 cestas distingu\303\255veis.
(i) Verifique se todos os ovos est\303\243o na mesma cesta.
(ii) Verifique se todos os ovos n\303\243o est\303\243o na mesma cesta.</Font></Text-field>
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<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field bookmark="ex2" style="Heading 2" foreground="[153,51,102]" layout="Heading 2"><Font foreground="[153,51,102]">2. <Font encoding="UTF-8">Independ\303\252ncia</Font></Font></Text-field></Title>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]" encoding="UTF-8">1. Temos componentes eletr\303\264nicos do mesmo tipo E, que operam em total independ\303\252ncia: sua taxa de falha \303\251 </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2L1EiPUYnRjJGNS9GOVEnbm9ybWFsRicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JlEkMC4xRidGMkY1Rj9GMkY1Rj8=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2L1EiPUYnRjJGNS9GOVEnbm9ybWFsRicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JlEkMC4xRidGMkY1Rj9GMkY1Rj8=</Equation><Font foreground="[153,51,102]">.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]">Determine a taxa de falhas dos seguintes sistemas:</Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal" alignment="centred"><Font foreground="[153,51,102]">(i) </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font foreground="[153,51,102]">     (ii) </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font foreground="[0,0,0]"> </Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]" encoding="UTF-8">2. Um avi\303\243o de tr\303\252s motores pode voar se seus motores laterais estiverem funcionando ou se seu motor intermedi\303\241rio estiver funcionando. A taxa de falha dos motores laterais \303\251 </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font foreground="[153,51,102]" encoding="UTF-8"> enquanto o do motor central \303\251 </Font><Equation executable="false" style="Text" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYnLUkjbW5HRiQ2JVEiMkYnRjUvRjlRJ25vcm1hbEYnRjJGNS8lLHBsYWNlaG9sZGVyR0Y0RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRk4vJSlzdHJldGNoeUdGTi8lKnN5bW1ldHJpY0dGTi8lKGxhcmdlb3BHRk4vJS5tb3ZhYmxlbGltaXRzR0ZOLyUnYWNjZW50R0ZOLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGZ24tRj42JVElMC4wMUYnRjVGQUY1RkE=</Equation><Font foreground="[153,51,102]">.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]">1. Consideramos dois eventos </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]"> e </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiQkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiQkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]" encoding="UTF-8"> e resumimos na tabela abaixo as probabilidades de interse\303\247\303\265es entre </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font foreground="[153,51,102]"> e </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font foreground="[153,51,102]"> :</Font></Text-field>
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Para mostrar isso</Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]" encoding="UTF-8">Jogamos uma moeda equiprob\303\241vel 4 vezes seguidas e anotamos em ordem a apar\303\252ncia de PILE ou FACE.

(i) Pr para obter o lan\303\247amento do PFPP.
(ii) Deixe o arremesso terminar FACE.
(iii) Pr que o arremesso tem 0,1,2,3,4 PILE.
(iv) Suponha que o arremesso tenha pelo menos uma PILHA e uma CARA.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]" encoding="UTF-8">Uma urna cont\303\251m 7 bolas, incluindo 4 vermelhas, 2 brancas e 1 preta: empatamos 2 bolas com desconto e estamos interessados \342\200\213\342\200\213nas su\303\255tes com repeti\303\247\303\243o </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font foreground="[153,51,102]"> de duas cores entre R,B,N.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]">(i) Pr para obter uma bola vermelha e uma bola branca.
(ii) Pr para obter duas bolas de cores diferentes.
(iii) Pr para obter 0.1.2 bolas brancas.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]" encoding="UTF-8">Numa popula\303\247\303\243o de </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]" encoding="UTF-8"> indiv\303\255duos discern\303\255veis, s\303\243o observados 2 casos de influenza: uma amostra aleat\303\263ria (n\303\243o ordenada) de 5 pessoas \303\251 coletada dentre </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]"> .</Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]" encoding="UTF-8">Fazemos p\303\243es de passas: em 500 g de massa, colocamos </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]" encoding="UTF-8"> rsecar migalhas de p\303\243o aleatoriamente e depois cortar a massa em 10 p\303\243es do mesmo peso. N\303\263s escolhemos um p\303\243o aleatoriamente.

Calcule a probabilidade de que o p\303\243o escolhido contenha pelo menos uma passa e determine </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]"> para que essa probabilidade seja maior que 0,99.</Font></Text-field>
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Queremos melhorar a confiabilidade do sistema </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font foreground="[153,51,102]" encoding="UTF-8"> e hesitamos entre duas estrat\303\251gias:</Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal" alignment="centred"><Font foreground="[153,51,102]">(i) </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkobWZlbmNlZEdGJDYmLUYjNi8tSSNtaUdGJDYnUSJFRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EtWzE1Myw1MSwxMDJdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYvUSJ+RidGN0Y6L0Y+USdub3JtYWxGJy8lJmZlbmNlR0Y8LyUqc2VwYXJhdG9yR0Y8LyUpc3RyZXRjaHlHRjwvJSpzeW1tZXRyaWNHRjwvJShsYXJnZW9wR0Y8LyUubW92YWJsZWxpbWl0c0dGPC8lJ2FjY2VudEdGPC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlZGQC1GQTYvUSI9RidGN0Y6RkRGRkZIRkpGTEZORlBGUi9GVVEsMC4yNzc3Nzc4ZW1GJy9GWEZnbkZARkBGMEY0RjdGOi8lLHBsYWNlaG9sZGVyR0Y2LyU2c2VsZWN0aW9uLXBsYWNlaG9sZGVyR0Y2Rj1GN0Y6RkRGQC1GQTYvUTQmRG91YmxlVmVydGljYWxCYXI7RidGN0Y6RkRGRkZIRkpGTEZORlBGUkZmbkZobkZALUYsNiYtRiM2LEYwRkBGQEZZRkBGQEYwRjdGOkZERjdGOkZELUYxNiNRIUYnRjdGOkZE">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</Equation><Font foreground="[153,51,102]">     (ii) </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font foreground="[153,51,102]"> </Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]" encoding="UTF-8">Determine a melhor estrat\303\251gia.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]" encoding="UTF-8">Uma sala cont\303\251m </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]"> pessoas</Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]">(i) <Font bold="true">Pr</Font> que </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1Eia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1Eia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]">  exatamente as pessoas nasceram em 01/01.
(il) Para que pelo menos 2 pessoas nascam em 01/01.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]" encoding="UTF-8">Pal\303\255ndromo \303\251 uma palavra lida da direita para a esquerda e da esquerda para a direita com o mesmo significado.

1. N\303\263s giramos </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW5HRiQ2JlEiMkYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2L1EifkYnRi9GMkY1LyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1JI21pR0YkNidRIm5GJy8lJ2l0YWxpY0dRJXRydWVGJ0YvRjIvRjZRJ2l0YWxpY0YnRi9GMkY1">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW5HRiQ2JlEiMkYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2L1EifkYnRi9GMkY1LyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1JI21pR0YkNidRIm5GJy8lJ2l0YWxpY0dRJXRydWVGJ0YvRjIvRjZRJ2l0YWxpY0YnRi9GMkY1</Equation><Font foreground="[153,51,102]" encoding="UTF-8"> independentemente, uma roleta com dois quadrados igualmente prov\303\241veis \342\200\213\342\200\2130 e 1.
(i) Pr para obter um pal\303\255ndromo.
(ii) Pr que a soma dos d\303\255gitos \303\251 igual a</Font><Font foreground="[153,51,102]"> </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1Eia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1Eia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]"> para </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY0LUkjbWlHRiQ2J1Eia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2L1EiPUYnRjJGNS9GOVEnbm9ybWFsRicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JlEiMEYnRjJGNUY/LUY8Ni9RIn5GJ0YyRjVGP0ZBRkNGRUZHRklGS0ZNL0ZQUSYwLjBlbUYnL0ZTRmZuLUY8Ni9RIixGJ0YyRjVGP0ZBL0ZERjFGRUZHRklGS0ZNRmVuL0ZTUSwwLjMzMzMzMzNlbUYnLUZVNiZRIjFGJ0YyRjVGP0ZYRmhuRlgtRjw2L1EoJmN0ZG90O0YnRjJGNUY/RkFGQ0ZFRkdGSUZLRk1GZW5GZ25GWEZobi1GVTYmUSIyRidGMkY1Rj9GWC1GLDYnUSJuRidGL0YyRjVGOEYyRjVGPw==">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</Equation><Font foreground="[153,51,102]"> .</Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]" encoding="UTF-8">3. Uma palavra \303\251 formada a partir de </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW5HRiQ2JlEiNEYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2L1EifkYnRi9GMkY1LyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1JI21pR0YkNidRIm5GJy8lJ2l0YWxpY0dRJXRydWVGJ0YvRjIvRjZRJ2l0YWxpY0YnRi9GMkY1">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW5HRiQ2JlEiNEYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2L1EifkYnRi9GMkY1LyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1JI21pR0YkNidRIm5GJy8lJ2l0YWxpY0dRJXRydWVGJ0YvRjIvRjZRJ2l0YWxpY0YnRi9GMkY1</Equation><Font foreground="[153,51,102]"> cartas incluindo </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW5HRiQ2JlEiMkYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2L1EifkYnRi9GMkY1LyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1JI21pR0YkNidRIm5GJy8lJ2l0YWxpY0dRJXRydWVGJ0YvRjIvRjZRJ2l0YWxpY0YnRi9GMkY1">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW5HRiQ2JlEiMkYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2L1EifkYnRi9GMkY1LyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1JI21pR0YkNidRIm5GJy8lJ2l0YWxpY0dRJXRydWVGJ0YvRjIvRjZRJ2l0YWxpY0YnRi9GMkY1</Equation><Font foreground="[153,51,102]"> letras A e </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW5HRiQ2JlEiMkYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2L1EifkYnRi9GMkY1LyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1JI21pR0YkNidRIm5GJy8lJ2l0YWxpY0dRJXRydWVGJ0YvRjIvRjZRJ2l0YWxpY0YnRi9GMkY1">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW5HRiQ2JlEiMkYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2L1EifkYnRi9GMkY1LyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1JI21pR0YkNidRIm5GJy8lJ2l0YWxpY0dRJXRydWVGJ0YvRjIvRjZRJ2l0YWxpY0YnRi9GMkY1</Equation><Font foreground="[153,51,102]"> letras B.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]" encoding="UTF-8">Jogamos uma moeda equiprob\303\241vel </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]" encoding="UTF-8"> times: o pedido \303\251 levado em considera\303\247\303\243o.

1. Observamos </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNigtRi82J1EibkYnRjJGNUY4RjtGMkY1RjgvJSxwbGFjZWhvbGRlckdGNEY7LyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGNUY4L0Y8USdub3JtYWxGJw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNigtRi82J1EibkYnRjJGNUY4RjtGMkY1RjgvJSxwbGFjZWhvbGRlckdGNEY7LyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGNUY4L0Y8USdub3JtYWxGJw==</Equation><Font foreground="[153,51,102]" encoding="UTF-8"> n\303\272mero de </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]" encoding="UTF-8">-lances que n\303\243o incluem 2 BATERIAS sucessivas.
Para mostrar isso  </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font foreground="[153,51,102]">  si </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2L1EvJkdyZWF0ZXJFcXVhbDtGJ0YyRjUvRjlRJ25vcm1hbEYnLyUmZmVuY2VHRjcvJSpzZXBhcmF0b3JHRjcvJSlzdHJldGNoeUdGNy8lKnN5bW1ldHJpY0dGNy8lKGxhcmdlb3BHRjcvJS5tb3ZhYmxlbGltaXRzR0Y3LyUnYWNjZW50R0Y3LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUS1JI21uR0YkNiZRIjNGJ0YyRjVGP0YyRjVGPw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2L1EvJkdyZWF0ZXJFcXVhbDtGJ0YyRjUvRjlRJ25vcm1hbEYnLyUmZmVuY2VHRjcvJSpzZXBhcmF0b3JHRjcvJSlzdHJldGNoeUdGNy8lKnN5bW1ldHJpY0dGNy8lKGxhcmdlb3BHRjcvJS5tb3ZhYmxlbGltaXRzR0Y3LyUnYWNjZW50R0Y3LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUS1JI21uR0YkNiZRIjNGJ0YyRjVGP0YyRjVGPw==</Equation><Font foreground="[153,51,102]">.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]" encoding="UTF-8">Um gene pode ter dois caracteres D ou R: sup\303\265e-se que cada gene tenha o car\303\241ter D com a mesma probabilidade </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]">.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]" encoding="UTF-8">1.Consideramos 2 genes independentes.
Pr que pelo menos um gene tem o car\303\241ter D.

2. Consideramos </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]" encoding="UTF-8"> genes em total independ\303\252ncia.
Pr que pelo menos 2 genes t\303\252m o car\303\241ter D.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]" encoding="UTF-8">1. Dois candidatos A e B em uma elei\303\247\303\243o obtida </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]" encoding="UTF-8"> cada voz.
Para que A esteja estritamente na lideran\303\247a durante a contagem dos votos.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]">2. </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW5HRiQ2JlEiMkYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2L1EifkYnRi9GMkY1LyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1JI21pR0YkNidRIm5GJy8lJ2l0YWxpY0dRJXRydWVGJ0YvRjIvRjZRJ2l0YWxpY0YnRi9GMkY1">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW5HRiQ2JlEiMkYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2L1EifkYnRi9GMkY1LyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1JI21pR0YkNidRIm5GJy8lJ2l0YWxpY0dRJXRydWVGJ0YvRjIvRjZRJ2l0YWxpY0YnRi9GMkY1</Equation><Font foreground="[153,51,102]"> as pessoas fazem fila no cinema, incluindo </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]" encoding="UTF-8"> tem uma nota de 5 \342\202\254 e </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]" encoding="UTF-8"> un bille \342\202\254 10: um ingresso de cinema custa \342\202\254 5 e n\303\243o h\303\241 trocas no caixa.
Pr que ningu\303\251m precisa esperar que a altera\303\247\303\243o seja devolvida.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]">Em um experimento </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2L1EiPUYnRjJGNS9GOVEnbm9ybWFsRicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JlEiNEYnRjJGNUY/RjJGNUY/">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2L1EiPUYnRjJGNS9GOVEnbm9ybWFsRicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JlEiNEYnRjJGNUY/RjJGNUY/</Equation><Font foreground="[153,51,102]"> ratos seguem independentemente um labirinto que termina em </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2L1EiPUYnRjJGNS9GOVEnbm9ybWFsRicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JlEiM0YnRjJGNUY/RjJGNUY/">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2L1EiPUYnRjJGNS9GOVEnbm9ybWFsRicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JlEiM0YnRjJGNUY/RjJGNUY/</Equation><Font foreground="[153,51,102]" encoding="UTF-8"> gaiolas equiprob\303\241veis: notamos </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNigtRi82J1Eia0YnRjJGNUY4RjtGMkY1RjgvJSxwbGFjZWhvbGRlckdGNEY7LyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGNUY4L0Y8USdub3JtYWxGJw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNigtRi82J1Eia0YnRjJGNUY4RjtGMkY1RjgvJSxwbGFjZWhvbGRlckdGNEY7LyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGNUY4L0Y8USdub3JtYWxGJw==</Equation><Font foreground="[153,51,102]"> o evento &quot;a gaiola </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1Eia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1Eia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]" encoding="UTF-8"> est\303\241 vazia&quot;.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]" encoding="UTF-8">A e B jogam PILE ou FACE com uma pe\303\247a igualmente prov\303\241vel: para cada jogada, A recebe um ponto se PILE aparecer e B um ponto se FACE aparecer. A aposta \303\251 de \342\202\254 100 e o vencedor \303\251 quem recebe o primeiro n\303\272mero </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiTkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiTkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]" encoding="UTF-8"> de pontos decididos previamente. O jogo \303\251 interrompido antes do final e est\303\241 faltando </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2L1EiPUYnRjJGNS9GOVEnbm9ybWFsRicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JlEiMkYnRjJGNUY/RjJGNUY/">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2L1EiPUYnRjJGNS9GOVEnbm9ybWFsRicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JlEiMkYnRjJGNUY/RjJGNUY/</Equation><Font foreground="[153,51,102]"> aponta para A para vencer, </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EibUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2L1EiPUYnRjJGNS9GOVEnbm9ybWFsRicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JlEiM0YnRjJGNUY/RjJGNUY/">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EibUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2L1EiPUYnRjJGNS9GOVEnbm9ybWFsRicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JlEiM0YnRjJGNUY/RjJGNUY/</Equation><Font foreground="[153,51,102]" encoding="UTF-8"> aponta para B para vencer: A e B querem compartilhar a propor\303\247\303\243o de suas chances de ganhar se o jogo terminar.</Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]" encoding="UTF-8">Representamos o final do jogo por um caminho na rede \342\204\225 \303\227 \342\204\225: i representa um ponto para A enquanto j representa um ponto para B.
Represente as posi\303\247\303\265es vencedoras de A e B nesta rede e calcule suas probabilidades. Deduzir o compartilhamento.</Font></Text-field>
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