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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,\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_) )]:\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######################################################### 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, RepeatName, 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, HighLightSubTree,\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_)]:\012RepeatName := proc(bb_,ww_) local k__,ww__:\012 ww__ := []:\012 for k__ from 1 to nops(ww_) do\012  if bb_[k__]=1 then ww__ := [op(ww__),ww_[k__]]\012                else ww__ := [op(ww__),seq(ww_[k__][l__],l__=1..bb_[k__])]\012                end if:\012  end do:\012 ww__:\012 end proc:\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:\012HighLightSubTree := proc(G_,V_,B_,o_,hl_,OPT_:=OPT0) local ij__,hs__,eps__,col__,sty__,tck__,n__,nr__,r__,vpq__,\012                                                           v__,p__,q__,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 vpq__ in V_ do\012  v__ := vpq__[1]: p__ := vpq__[2]: q__ := vpq__[3]:\012  if p__ = 0 then o__ := o_\012             else  nr__ := v2nr(v__,B_,p__):\012                   r__  := nr__[2]:\012                   o__ := OO__[p__][r__]:\012             end if:\012  leaf__ := [o__,o__]:\012  for n__ from p__+1 to q__ 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(display([ 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(display([G_,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, DecodeV, DecodeM,\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           event_ta_lessorequal, event_ta_greater, event_ta_equal;\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:\012DecodeV := proc(ind_) local L__,vpq__:\012 L__ := StringTools[Explode](ind_):\012 vpq__ := []:\012 if nops(L__) = 2 \012  then if      L__[2] = &quot;#&quot;  then vpq__ := [[parse(L__[1])],0,1]\012       else if L__[1] &lt;&gt; &quot;#&quot; then vpq__ := [map(parse,L__),0,2]\012       end if end if\012  else if L__[1] = &quot;#&quot; then vpq__ := [map(parse,[L__[3],L__[2]]),1,2]\012       end if\012  end if:\012 vpq__:\012 end proc:\012DecodeM := proc(ind_) local L__,ij__:\012 L__ := StringTools[Explode](ind_):\012 ij__ := []:\012 if nops(L__) = 2 \012  then  if      L__[1] = &quot;#&quot; then ij__ := [3,parse(L__[2])]\012        else if L__[2] = &quot;#&quot; then ij__ := [parse(L__[1]),3]\012        else ij__ := map(parse,L__)\012        end if end if:\012  end if:\012 ij__:\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_,log_:=&quot;&quot;)\012 false:\012 end proc:\012event_full := proc(v_,EVENT_,B_,BB_,WW_,log_:=&quot;&quot;)\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:\012event_ta_lessorequal := proc(v_,EVENT_,B_,BB_,WW_,log_:=&quot;&quot;) local k__,boo__:\012 boo__ := []:\012 for k__ from 1 to min(nops(v_),EVENT_[1]) do\012  boo__ := [op(boo__),evalb(WW_[k__][v2nr(v_,B_,k__)[2]] in EVENT_[2])]:\012  end do:\012 convert(boo__,`or`):\012 end proc:\012event_ta_greater := proc(v_,EVENT_,B_,BB_,WW_,log_:=&quot;&quot;)\012 evalb(`not`(event_ta_lessorequal(v_,EVENT_,B_,BB_,WW_))):\012 end proc:\012event_ta_equal := proc(v_,EVENT_,B_,BB_,WW_,log_:=&quot;&quot;) local k__,boo__,n__:\012 boo__ := []: n__ := EVENT_[1]: \012 if n__ &gt; nops(v_) \012  then boo__ := `false`\012  else for k__ from 1 to n__-1 do\012        boo__ := [op(boo__),evalb(WW_[k__][v2nr(v_,B_,k__)[2]] in EVENT_[2])]:\012        end do:\012       boo__ := convert(boo__,`or`):\012       boo__ := evalb(not(boo__) and evalb(WW_[n__][v2nr(v_,B_,n__)[2]] in EVENT_[2])):\012  end if:\012 boo__:\012 end proc:\012end module:                                                                                                                                                                                                                                                                                                                              \012                                                                         \012######################################################## FILM ##################################################################            \012\012PROBII_CO := module()                                                                                      \012\012  uses     DocumentTools, StringTools, ListTools, plots, LinearAlgebra, \012           AnimationII, AlgLin, Analyse, Geometrie, ProbComb, ProbMisc; \012  export   TA_E, TA_T, TA_P,\012           PC_E, PC_T, PC_P,\012           BA_E, BA_T, BA_P,\012           VP_E, VP_T, VP_P;\012  local    Paragraphe;\012  option package;\012\012########################################################\012univ   := [[1,1],['P','F']]:                                                                              \012event_i   := [[{},{}],event_empty,&quot;&quot;]:                                                                    \012event_ii  := [[2,{'P'}],event_ta_greater,&quot;&quot;]:                                                         \012TA_E := table([]):                                                                                        \012TA_E[&quot;i&quot;]   := [5,2,univ,event_i]:                                                                        \012TA_E[&quot;ii&quot;]  := [5,2,univ,event_ii]:                                                                       \012TA_T := &quot;i&quot;:                                                                                              \012TA_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\012bb := Up: bf := [seq(rule_taar,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),[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:\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,[ [PRTpl,PRTpl],[PRTnn,PRTpc],[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,WW]: Graphs := G:\012table([ &quot;c&quot; = Calcs , &quot;g&quot; = Graphs ]):\012\012end proc:\012\012########################################################\012\012PC_Pr0 := table([&quot;1#&quot;=0.5,&quot;#11#&quot;=0.2,&quot;#1&quot;=0.3]): PC_Pr  := copy(Pr0):                                           \012univ_i  := [ PC_Pr0,[&quot;V&quot;,&quot;M&quot;] ]:                                                                             \012univ_ii := [ PC_Pr ,[&quot;V&quot;,&quot;M&quot;] ]:                                                                             \012event_i  := [[{},{}],event_empty,&quot;&quot;]:                                                                     \012event_ii := [[{},{}],event_full,&quot;&quot;]:                                                                      \012PC_E := table([]):                                                                                        \012PC_E[&quot;i&quot;]  := [2,[2,2],univ_i,event_i]:                                                                   \012PC_E[&quot;ii&quot;] := [2,[2,2],univ_ii,event_ii]:                                                                 \012PC_T := &quot;i&quot;:                                                                                              \012PC_P := proc(PAR,T) global o0,AT,OPT,CHX:                                                                 \012\012JOK := [&quot;#&quot;]: CHX := {1,2}:\012\012p := PAR[1]: nn := PAR[2]: UNIV := PAR[3]: EVENT := PAR[4]:\012Up := copy(UNIV[1]): Us := UNIV[2]: Ed := EVENT[1]: Er := EVENT[2]: Eb := EVENT[3]:\012\012bb1  := [Up[&quot;1#&quot;],Up[&quot;2#&quot;]]: \012bb2  := [ [Up[&quot;#11#&quot;],Up[&quot;#21#&quot;]],[Up[&quot;#12#&quot;],Up[&quot;#22#&quot;]] ]:\012bb := bb1:  bf := [(b,j) -&gt; bb2[j]]: BF := [bb,op(bf)]:\012\012ww_1 := [Us[1],cat(Us[1],c)]: \012ww_2 := [ [cat(Us[2],&quot;|&quot;,Us[1]),cat(Us[2],&quot;c&quot;,&quot;|&quot;,Us[1])],[cat(Us[2],&quot;|&quot;,Us[1],&quot;c&quot;),cat(Us[2],&quot;c&quot;,&quot;|&quot;,Us[1],&quot;c&quot;)] ]:\012ww := ww_1: wf := [(w,j) -&gt; ww_2[j]]:  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 P2 := [Up[&quot;11&quot;],Up[&quot;12&quot;],Up[&quot;21&quot;],Up[&quot;22&quot;]]:\012                     W2 := [&quot;V &amp; M&quot;,&quot;V &amp; Mc&quot;,&quot;Vc &amp; M&quot;,&quot;Vc &amp; Mc&quot;]:\012                     PW := Matrix(3,2,[[PW0,PW0],[[P2,W2],[P2,W2]],[PW0,PW0]]):\012 else if T=&quot;ii&quot; then P2 := [Up[&quot;11&quot;],Up[&quot;12&quot;],Up[&quot;21&quot;],Up[&quot;22&quot;]]:\012                     W2 := [&quot;V &amp; M&quot;,&quot;V &amp; Mc&quot;,&quot;Vc &amp; M&quot;,&quot;Vc &amp; Mc&quot;]:\012                     PW := Matrix(3,2,[[PW0,PW0],[[P2,W2],[P2,W2]],[PW0,PW0]]):\012 end if end if:\012if       T=&quot;i&quot;  then PRT := Matrix(3,2,[ [PRTcl,PRTcl],[PRTio,PRTio],[PRTii,PRTii] ])\012 else if T=&quot;ii&quot; then PRT := Matrix(3,2,[ [PRTcl,PRTcl],[PRTio,PRTio],[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\012BA_Pr0 := table([&quot;1#&quot;=0.1,&quot;#11#&quot;=0.2,&quot;#22#&quot;=0.3]): Pr  := copy(Pr0):                                         \012univ_i  := [ BA_Pr0,[&quot;M&quot;,&quot;T&quot;] ]:                                                                             \012univ_ii := [ BA_Pr0 ,[&quot;T&quot;,&quot;M&quot;] ]:                                                                             \012event_i  := [[{},{}],event_empty,&quot;&quot;]:                                                                     \012event_ii := [[{},{}],event_full,&quot;&quot;]:                                                                      \012BA_E := table([]):                                                                                        \012BA_E[&quot;i&quot;]  := [2,[2,2],univ_i,event_i]:                                                                   \012BA_E[&quot;ii&quot;] := [2,[2,2],univ_ii,event_ii]:                                                                 \012BA_T := &quot;i&quot;:                                                                                              \012BA_P := proc(PAR,T) global o0,AT,OPT,CHX:                                                                 \012\012JOK := [&quot;#&quot;]: CHX := {1,2}:\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\012if       T = &quot;i&quot;  then bb1  := [Up[&quot;1#&quot;],Up[&quot;2#&quot;]]:\012                       bb2  := [ [Up[&quot;#11#&quot;],Up[&quot;#21#&quot;]],[Up[&quot;#12#&quot;],Up[&quot;#22#&quot;]] ]:\012 else if T = &quot;ii&quot; then bb1  := [Up[&quot;#1&quot;],Up[&quot;#2&quot;]]: \012                       bb2  := [ [Up[&quot;1##1&quot;],Up[&quot;2##1&quot;]],[Up[&quot;1##2&quot;],Up[&quot;2##2&quot;]] ]:\012 end if end if:\012bb := bb1:  bf := [(b,j) -&gt; bb2[j]]: \012BF := [bb,op(bf)]:\012\012ww_1 := [Us[1],cat(Us[1],c)]: \012ww_2 := [ [cat(Us[2],&quot;|&quot;,Us[1]),cat(Us[2],&quot;c&quot;,&quot;|&quot;,Us[1])],[cat(Us[2],&quot;|&quot;,Us[1],&quot;c&quot;),cat(Us[2],&quot;c&quot;,&quot;|&quot;,Us[1],&quot;c&quot;)] ]:\012ww := ww_1: wf := [(w,j) -&gt; ww_2[j]]:  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 P2 := [Up[&quot;11&quot;],Up[&quot;12&quot;],Up[&quot;21&quot;],Up[&quot;22&quot;]]:\012                     W2 := [&quot;V &amp; M&quot;,&quot;V &amp; Mc&quot;,&quot;Vc &amp; M&quot;,&quot;Vc &amp; Mc&quot;]:\012                     PW := Matrix(3,2,[[PW0,PW0],[[P2,W2],[P2,W2]],[PW0,PW0]]):\012 else if T=&quot;ii&quot; then P2 := [Up[&quot;11&quot;],Up[&quot;12&quot;],Up[&quot;21&quot;],Up[&quot;22&quot;]]:\012                     W2 := [&quot;V &amp; M&quot;,&quot;V &amp; Mc&quot;,&quot;Vc &amp; M&quot;,&quot;Vc &amp; Mc&quot;]:\012                     PW := Matrix(3,2,[[PW0,PW0],[[P2,W2],[P2,W2]],[PW0,PW0]]):\012 end if end if:\012if       T=&quot;i&quot;  then PRT := Matrix(3,2,[ [PRTcl,PRTcl],[PRTio,PRTio],[PRTii,PRTii] ])\012 else if T=&quot;ii&quot; then PRT := Matrix(3,2,[ [PRTcl,PRTcl],[PRTio,PRTio],[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\012VP_E := [0.9,0.9]:   \012VP_T := &quot;&quot;:                                                                                    \012VP_P := proc(PAR,T)                                                              \012\012s1 := PAR[1]: s2 := PAR[2]:\012\012tau1 := p -&gt; s1*p/(s1*p+(1-s2)*(1-p)):\012tau2 := p -&gt; s2*(1-p)/(s2*(1-p)+(1-s1)*p):\012G1 := plot(tau1(p),p=0..1,color=&quot;DarkRed&quot;):\012G2 := plot(tau2(p),p=0..1,color=&quot;DarkBlue&quot;):\012\012VS2D := table([ &quot;v&quot;=default, &quot;s&quot;=constrained, &quot;a&quot;=normal ]):\012G := display( [ G1,G2 ], view=VS2D[&quot;v&quot;], scaling = VS2D[&quot;s&quot;], axes = VS2D[&quot;a&quot;] ):\012Calcs := [tau1(p),tau2(p)]: 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(PROBII_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,7]],[[roman,9],[roman,7]]]:\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]]):\012\012HL := [[&quot;Crimson&quot;,'solid',1],[&quot;BlueViolet&quot;,'solid',1]]:\012\012IJ := [1,8]: EPS := 0.1: 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\012IND  := {&quot;1#&quot;,&quot;2#&quot;,&quot;#1&quot;,&quot;#2&quot;,&quot;11&quot;,&quot;12&quot;,&quot;21&quot;,&quot;22&quot;,&quot;#11#&quot;,&quot;#21#&quot;,&quot;#12#&quot;,&quot;#22#&quot;,&quot;1##1&quot;,&quot;2##1&quot;,&quot;1##2&quot;,&quot;2##2&quot;}:   \012\012ProbCond := proc(Pr0_,Pr_)                                                                                \012  local known__,known0__,stree__,stree0__,matpr__,matpr0__,unknown__,unknown0__,solved__,                 \012        ind__,ij__,vpq__,eq__,eq0__,eq1__,eqs__,sol__,k__:                                                \012  global IND,EQ:                                                                                          \012\012known0__ := {indices(Pr0_,'nolist')}:\012unknown0__ := IND minus known0__:\012for ind__ in unknown0__ do Pr0_[ind__] := &quot;?&quot; end do:\012\012matpr0__ := Matrix(3,3,0):\012matpr0__[3,3] := 1:\012for ind__ in known0__ do \012 ij__ := DecodeM(ind__):\012 if ij__ &lt;&gt; [] then matpr0__[op(ij__)] := evalf(Pr0_[ind__],3) end if:\012 end do:\012\012stree0__ := []:\012for ind__ in known0__ do \012 vpq__ := DecodeV(ind__):\012 if vpq__ &lt;&gt; [] then stree0__ := [op(stree0__),DecodeV(ind__)] end if:\012 end do:\012\012EQ := [ [{Pr_[&quot;1#&quot;]+Pr_[&quot;2#&quot;]=1},{&quot;1#&quot;,&quot;2#&quot;}],\012        [{Pr_[&quot;#1&quot;]+Pr_[&quot;#2&quot;]=1},{&quot;#1&quot;,&quot;#2&quot;}],\012        [{Pr_[&quot;11&quot;]+Pr_[&quot;12&quot;]=Pr_[&quot;1#&quot;]},{&quot;11&quot;,&quot;12&quot;,&quot;1#&quot;}],\012        [{Pr_[&quot;21&quot;]+Pr_[&quot;22&quot;]=Pr_[&quot;2#&quot;]},{&quot;21&quot;,&quot;22&quot;,&quot;2#&quot;}],\012        [{Pr_[&quot;11&quot;]+Pr_[&quot;21&quot;]=Pr_[&quot;#1&quot;]},{&quot;11&quot;,&quot;21&quot;,&quot;#1&quot;}],\012        [{Pr_[&quot;12&quot;]+Pr_[&quot;22&quot;]=Pr_[&quot;#2&quot;]},{&quot;12&quot;,&quot;22&quot;,&quot;#2&quot;}],\012        [{Pr_[&quot;#11#&quot;]*Pr_[&quot;1#&quot;]=Pr_[&quot;11&quot;]},{&quot;#11#&quot;,&quot;1#&quot;,&quot;11&quot;}],\012        [{Pr_[&quot;#12#&quot;]*Pr_[&quot;2#&quot;]=Pr_[&quot;21&quot;]},{&quot;#12#&quot;,&quot;2#&quot;,&quot;21&quot;}],\012        [{Pr_[&quot;#21#&quot;]*Pr_[&quot;1#&quot;]=Pr_[&quot;12&quot;]},{&quot;#21#&quot;,&quot;1#&quot;,&quot;12&quot;}],\012        [{Pr_[&quot;#22#&quot;]*Pr_[&quot;2#&quot;]=Pr_[&quot;22&quot;]},{&quot;#22#&quot;,&quot;2#&quot;,&quot;22&quot;}],\012        [{Pr_[&quot;1##1&quot;]*Pr_[&quot;#1&quot;]=Pr_[&quot;11&quot;]},{&quot;1##1&quot;,&quot;#1&quot;,&quot;11&quot;}],\012        [{Pr_[&quot;1##2&quot;]*Pr_[&quot;#2&quot;]=Pr_[&quot;12&quot;]},{&quot;1##2&quot;,&quot;#2&quot;,&quot;12&quot;}],\012        [{Pr_[&quot;2##1&quot;]*Pr_[&quot;#1&quot;]=Pr_[&quot;21&quot;]},{&quot;2##1&quot;,&quot;#1&quot;,&quot;21&quot;}],\012        [{Pr_[&quot;2##2&quot;]*Pr_[&quot;#2&quot;]=Pr_[&quot;22&quot;]},{&quot;2##2&quot;,&quot;#2&quot;,&quot;22&quot;}],\012        [{Pr[&quot;#11#&quot;]*Pr[&quot;1#&quot;]+Pr[&quot;#12#&quot;]*Pr[&quot;2#&quot;]=Pr[&quot;#1&quot;]},{&quot;#11#&quot;,&quot;#12#&quot;,&quot;1#&quot;,&quot;2#&quot;,&quot;#1&quot;}],\012        [{Pr[&quot;#21#&quot;]*Pr[&quot;1#&quot;]+Pr[&quot;#22#&quot;]*Pr[&quot;2#&quot;]=Pr[&quot;#2&quot;]},{&quot;#21#&quot;,&quot;#22#&quot;,&quot;1#&quot;,&quot;2#&quot;,&quot;#2&quot;}] ]:\012eq__ := {seq(k__,k__=1..nops(EQ))}:\012\012known__ := known0__: stree__ := []: eqs__ := eq__:\012while eqs__ &lt;&gt; {} do\012 eq0__ := {}:\012 for k__ in eq__ do\012  if nops(EQ[k__][2] minus known__)=0 then eq0__ := eq0__ union {k__}: end if:\012  end do:\012 eq__ := eq__ minus eq0__:\012 eq1__ := {}:\012 for k__ in eq__ do\012  if nops(EQ[k__][2] minus known__)=1 then eq1__ := eq1__ union {k__}:\012                                           sol__ := solve(EQ[k__][1]):\012                                           known__ := known__ union EQ[k__][2]:\012                                           ind__ := op(op(1,op(sol__))):\012                                           vpq__ := DecodeV(ind__):\012                                           if vpq__ &lt;&gt; [] then stree__ := [op(stree__),vpq__] end if:\012                                           Pr_[ind__] := evalf(op(2,op(sol__)),3):\012                                           end if:\012  end do:\012  eq__ := eq__ minus eq1__:\012 eqs__ := eq0__ union eq1__:\012 end do:\012unknown__ := IND minus known__:\012for ind__ in unknown__ do Pr_[ind__] := &quot;?&quot; end do:\012\012matpr__ := Matrix(3,3,0):\012matpr__[3,3] := 1:\012for ind__ in known__ do \012 ij__ := DecodeM(ind__):\012 if ij__ &lt;&gt; [] then matpr__[op(ij__)] := Pr_[ind__] end if:\012 end do:\012\012solved__ := []:\012for ind__ in known__ do solved__ := [op(solved__),[ind__,Pr_[ind__]]] end do:\012\012[[Pr0_,matpr0__,stree0__],[Pr_,matpr__,stree__],[solved__,unknown__]]:\012end proc:\012\012########################################################\012\012#exw1\012Do(%exw1TARp = 0.1):\012Do(%exw1TARalpha = 97):\012Do(%exw1TARbeta = 89):\012Do(%exw1TARn = 3):\012Do(%exw1TARm = 3):\012Do(%exw1LSB1 = &quot;pollu\303\251e&quot;):\012Do(%exw1LSB1 = &quot;se trompe&quot;):\012Do(%exw1LSB1 = &quot;pollu\303\251e&quot;):\012\012Do(%exw1TAR21 = &quot;&quot;):\012Do(%exw1TAR22 = &quot;&quot;):\012Do(%exw1MEC21 = &quot;&quot;):\012Do(%exw1MEC22 = &quot;&quot;):\012\012Do(%exw1TAR3 = &quot;&quot;):\012Do(%exw1MEC3 = &quot;&quot;):"/>
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(i) Pr para obter a primeira PILHA antes do 4\302\272 arremesso.
(ii) Fa\303\247a pelo menos 4 fotos com tinta antes de obter a primeira PILHA.
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]" encoding="UTF-8">Jogamos um dado de seis lados equiprob\303\241vel um n\303\272mero indeterminado de vezes de forma independente: notamos </Font><Equation executable="false" style="Text" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EnJiM5Mzc7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyU2c2VsZWN0aW9uLXBsYWNlaG9sZGVyR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYnLUYvNiZRIm5GJy9GM0Y6RjUvRjxRJ2l0YWxpY0YnRkNGNS8lLHBsYWNlaG9sZGVyR0Y6RkQvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y1Rjs=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EnJiM5Mzc7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyU2c2VsZWN0aW9uLXBsYWNlaG9sZGVyR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYnLUYvNiZRIm5GJy9GM0Y6RjUvRjxRJ2l0YWxpY0YnRkNGNS8lLHBsYWNlaG9sZGVyR0Y6RkQvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y1Rjs=</Equation><Font foreground="[153,51,102]" encoding="UTF-8"> o evento &quot;os 5 primeiros s\303\243o classificados </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]"> &quot; e </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]"> o evento &quot;o 5 aparece antes do 2&quot;.</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="[153,51,102]">     (iii) </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KVEjcHJGJy8lJWJvbGRHUSV0cnVlRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGPC1JKG1mZW5jZWRHRiQ2Ji1GIzYmLUYsNihRIkFGJy9GM0YxRjVGOC8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdGMS9GO1EnaXRhbGljRidGNUY4L0Y7USdub3JtYWxGJ0Y1RjhGTEY1RjhGTA==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KVEjcHJGJy8lJWJvbGRHUSV0cnVlRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdGNC8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGPC1JKG1mZW5jZWRHRiQ2Ji1GIzYmLUYsNihRIkFGJy9GM0YxRjVGOC8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdGMS9GO1EnaXRhbGljRidGNUY4L0Y7USdub3JtYWxGJ0Y1RjhGTEY1RjhGTA==</Equation></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">O universo adaptado ao problema \303\251 o conjunto \316\251 dos seguintes </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 # dDesigna qualquer resultado, exceto 5.</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]">Existem 2 caminhos que correspondem ao evento &quot;mesmo sexo&quot;:</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font foreground="[153,51,102]" encoding="UTF-8">2. Dans une loterie on tire sans remise 3 nombres parmi les nombres 1 , 2 , \342\213\257 , 20 : il y a 5 bons num\303\251ros parmi les 20.</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font bold="true" foreground="[153,51,102]">Pr</Font><Font foreground="[153,51,102]" encoding="UTF-8"> d'obtenir 2 bons num\303\251ros exactement.</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 \303\241rvore de probabilidades \303\251 composta de 3 n\303\255veis, que correspondem \303\240s escolhas dos 3 n\303\272meros: os resultados \303\272teis s\303\243o </Font><Font size="10" foreground="[0,51,0]" italic="true">B</Font><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> = &quot;n\303\272mero correto&quot; e </Font><Font size="10" foreground="[0,51,0]" italic="true">M</Font><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> = &quot;n\303\272mero errado&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]">Ha sim  </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">  caminhos que correspondem ao evento &quot;exatamente 2 n\303\272meros corretos&quot; e todos t\303\252m a mesma probabilidade</Font><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" underline="true" foreground="[0,51,0]" encoding="UTF-8">Nota: tamb\303\251m \303\251 poss\303\255vel fazer um c\303\241lculo por equiprobabilidade.</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">Em uma popula\303\247\303\243o, sabemos que a probabilidade de nascimento de um menino \303\251 de 0,52 e, al\303\251m disso, 2% das meninas e 1% dos meninos t\303\252m uma luxa\303\247\303\243o do quadril.</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. N\303\263s notamos </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]"> o evento &quot;nascimento de uma filha&quot; e </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]" encoding="UTF-8"> o evento &quot;ter uma luxa\303\247\303\243o do quadril&quot;. Elabore a tabela de probabilidades de interse\303\247\303\243o 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]"> . Os eventos </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]"> e </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]" encoding="UTF-8"> eles s\303\243o independentes?
2. Calcule a probabilidade de um rec\303\251m-nascido com um deslocamento ser:
(i) uma menina (ii) um menino</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 declara\303\247\303\243o d\303\241 </Font><Equation executable="false" style="2D Math" input-equation="" 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(i) Pr que esta sequ\303\252ncia est\303\241 aumentando estritamente.
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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">(i) Existem tantas sequ\303\252ncias estritamente crescentes de 5 n\303\272meros entre 10 quanto partes com 5 elementos entre 10, portanto, </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" underline="true" foreground="[0,51,0]" encoding="UTF-8">M\303\251todo 1</Font><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> : condicionamento intuitivo.
  N\303\263s restringimos o universo \316\251 para todos \316\251 ' suites sem repeti\303\247\303\243o de 3 de 8: </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></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]">(i)O evento </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUklbXN1YkdGJDYlLUkjbWlHRiQ2KFEiQUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYpLUYvNihRIm5GJ0YyRjVGOEY7Rj5GMkY1RjhGOy8lLHBsYWNlaG9sZGVyR0Y3Rj4vJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0YyRjhGOy9GP1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUklbXN1YkdGJDYlLUkjbWlHRiQ2KFEiQUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYpLUYvNihRIm5GJ0YyRjVGOEY7Rj5GMkY1RjhGOy8lLHBsYWNlaG9sZGVyR0Y3Rj4vJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0YyRjhGOy9GP1Enbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> \303\251 um eventos dos seguintes </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]"> , que pode ser vantajosamente codificado por </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEmRkZGRkZGJy8lJXNpemVHUSMxMEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRKVswLDUxLDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGL0Y1RjgvRjxRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEmRkZGRkZGJy8lJXNpemVHUSMxMEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRKVswLDUxLDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGL0Y1RjgvRjxRJ25vcm1hbEYn</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> porque todos os resultados que se seguem ao quinto s\303\243o aceit\303\241veis.</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">(ii) Nos limitamos ao m\303\251todo por condicionamento intuitivo. Isso consiste em restringir o universo \316\251 para todos \316\251 ' seq\303\274\303\252ncias que come\303\247am no rank 6: a probabilidade procurada \303\251</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]"> .</Font></Text-field>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]">Uma jarra </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]" encoding="UTF-8"> cont\303\251m 1 bola vermelha e 2 bolas pretas, uma urna </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EjSUlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2ZvcmVncm91bmRHUS1bMTUzLDUxLDEwMl1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YyRjUvRjlRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EjSUlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2ZvcmVncm91bmRHUS1bMTUzLDUxLDEwMl1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YyRjUvRjlRJ25vcm1hbEYn</Equation><Font foreground="[153,51,102]" encoding="UTF-8"> cont\303\251m 2 bolas vermelhas e 1 bola preta.
Desenhamos aleatoriamente (equiprobabilidade) uma bola na urna </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]"> ou </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EjSUlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2ZvcmVncm91bmRHUS1bMTUzLDUxLDEwMl1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YyRjUvRjlRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EjSUlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2ZvcmVncm91bmRHUS1bMTUzLDUxLDEwMl1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YyRjUvRjlRJ25vcm1hbEYn</Equation><Font foreground="[153,51,102]"> e tiramos uma bola vermelha.
Para que a bola saia da urna </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EjSUlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2ZvcmVncm91bmRHUS1bMTUzLDUxLDEwMl1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YyRjUvRjlRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EjSUlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2ZvcmVncm91bmRHUS1bMTUzLDUxLDEwMl1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YyRjUvRjlRJ25vcm1hbEYn</Equation><Font foreground="[153,51,102]"> .</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]">Notamos </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiUkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiUkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]"> o evento &quot;chute uma bola vermelha&quot;, </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiSUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEiSUYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]"> o evento &quot;atirar na urna I&quot; e </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEjSUlGJy8lJXNpemVHUSMxMEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRKVswLDUxLDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGL0Y1RjgvRjxRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEjSUlGJy8lJXNpemVHUSMxMEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRKVswLDUxLDBdRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGL0Y1RjgvRjxRJ25vcm1hbEYn</Equation><Font size="10" foreground="[0,51,0]">  o evento &quot;atirar na urna II&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]">Temos  </Font><Equation executable="false" style="2D Math" input-equation="" 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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]" encoding="UTF-8">Suponha que qualquer indiv\303\255duo da popula\303\247\303\243o esteja b\303\252bado com a 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]">Calcular probabilidades condicionais </Font><Equation executable="false" style="2D Math" input-equation="" 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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]" encoding="UTF-8">No caso de este rio transbordar, um funcion\303\241rio municipal \303\251 respons\303\241vel por tomar  </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font bold="true" foreground="[128,0,128]"> <EC-TextArea id="exw1TARn" 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 foreground="[153,51,102]"> <Font encoding="UTF-8">recolha amostras de \303\241gua no dia seguinte e analise cada amostra separadamente.

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(iii) A declara\303\247\303\243o pergunta, dependendo do caso, a probabilidade de um dos seguintes eventos:</Font></Text-field>
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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal" alignment="centred"><EC-RadioButton id="exw1RAB2" caption="2. Solution" groupname="exw1RAB" fontcolor="[0,0,0]" fillcolor="[255,255,255]" enabled="true" visible="true" selected="false"><MapleCode action="click-event-handler">use DocumentTools in 

a := (p,n,k,alpha,beta) -&gt; p*(alpha^k)*((1-alpha)^(n-k)):
b := (p,n,k,alpha,beta) -&gt; (1-p)*((1-beta)^k)*(beta^(n-k)):
c := (p,n,k,alpha,beta) -&gt; a(p,n,k,alpha,beta) + b(p,n,k,alpha,beta): 
pr1 := (p,n,k,alpha,beta) -&gt; a(p,n,k,alpha,beta)/c(p,n,k,alpha,beta):
pr2 := (p,n,k,alpha,beta) -&gt; b(p,n,k,alpha,beta)/c(p,n,k,alpha,beta):

p0 := parse(GetProperty(exw1TARp,'value')):
n0 := parse(GetProperty(exw1TARn,'value')):
m0 := parse(GetProperty(exw1TARm,'value')):
alpha0 := parse(GetProperty(exw1TARalpha,'value'))/100:
beta0 := parse(GetProperty(exw1TARbeta,'value'))/100:
analyse := GetProperty(exw1LSB1,'value'):
if analyse = &quot;pollu\303\251e&quot; then k0 := m0 else k0 := n0-m0 end if:
pr21 := p -&gt; pr1(p,n0,k0,alpha0,beta0):
pr22 := p -&gt; pr2(p,n0,k0,alpha0,beta0):

Do(%exw1TAR21 = evalf[5](pr21(p0))):
Do(%exw1TAR22 = evalf[5](pr22(p0))):
Do(%exw1MEC21 = simplify(pr21(x))): 
Do(%exw1MEC22 = simplify(pr22(x))): 

end use; 
</MapleCode></EC-RadioButton></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">Usamos a f\303\263rmula de probabilidade condicional</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">bem como as f\303\263rmulas</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]">Ha sim </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]"> maneiras de escolher </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEia0YnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEia0YnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> an\303\241lises em quest\303\243o entre </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEibkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEibkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]"> , e cada escolha tem a mesma 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]" encoding="UTF-8"> , ent\303\243o</Font></Text-field>
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size="10" foreground="[0,51,0]">  como acima: porque o complementar do 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]"> &quot; </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEia0YnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEia0YnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> an\303\241lises sobre </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEibkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEibkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> diga que a fonte \303\251 polu\303\255do &quot;n\303\243o \303\251&quot; </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEia0YnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEia0YnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> an\303\241lise sobre </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEibkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEibkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> diga que a fonte n\303\243o est\303\241 polu\303\255da &quot;.
Voc\303\252 precisa ver as coisas do seguinte \303\242ngulo: 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]"> &quot; </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEia0YnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEia0YnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> an\303\241lise sobre </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEibkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEibkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> dizer que a fonte est\303\241 polu\303\255da &quot;\303\251 igual ao 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]"> &quot; 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size="10" foreground="[0,51,0]"> maneiras de escolher </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEia0YnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEia0YnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> an\303\241lises em quest\303\243o entre </Font><Equation executable="false" style="2D Math" input-equation="" 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rspace='0.2222222em'&gt;&amp;minus;&lt;/mo&gt;&lt;mn fontweight='normal'&gt;1&lt;/mn&gt;&lt;mo fontweight='normal' lspace='0.2222222em' rspace='0.2222222em'&gt;&amp;plus;&lt;/mo&gt;&lt;mi fontweight='normal'&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mn fontweight='normal'&gt;42659&lt;/mn&gt;&lt;mo fontweight='normal' lspace='0.0em' rspace='0.0em'&gt;&amp;InvisibleTimes;&lt;/mo&gt;&lt;mi fontweight='normal'&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mo fontweight='normal' lspace='0.2222222em' rspace='0.2222222em'&gt;&amp;minus;&lt;/mo&gt;&lt;mn fontweight='normal'&gt;42875&lt;/mn&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mstyle&gt;&lt;/math&gt;"></EC-MathContainer>  .</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
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<Input><Text-field style="Text" layout="Normal" alignment="centred"><EC-RadioButton id="exw1RAB3" caption="3. R\303\251ponse" groupname="exw1RAB" fontcolor="[0,0,0]" fillcolor="[255,255,255]" enabled="true" visible="true" selected="true"><MapleCode action="click-event-handler">use DocumentTools in 

maire := GetProperty(exw1LSB2,'value'):
eau := GetProperty(exw1LSB3,'value'):

test := evalb( (maire=&quot;ait raison&quot; and eau=&quot;pollu\303\251e&quot;) or (maire=&quot;se trompe&quot; and eau=&quot;saine&quot;) ):
if test then res1 := GetProperty(exw1TAR21,'value'):
	        res2 := MathML[ImportModified](GetProperty(exw1MEC21,'value')):
        else res1 := GetProperty(exw1TAR22,'value'):
	        res2 := MathML[ImportModified](GetProperty(exw1MEC22,'value')):
	   end if:
	   
Do(%exw1TAR3 = res1):
Do(%exw1MEC3 = res2): 

end use; </MapleCode></EC-RadioButton></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 probabilidade procurada \303\251 <EC-TextArea id="exw1TAR3" enabled="true" visible="true" visiblecharacterwidth="10" visiblerows="1" fontcolor="[0,0,0]" fillcolor="[255,255,255]" contents="" editable="false" wrapping="true" show-border="true" password="false"></EC-TextArea></Font><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]">
<Font encoding="UTF-8">A fun\303\247\303\243o usada \303\251   <EC-MathContainer id="exw1MEC3" pixel-width="150" pixel-height="50" fillcolor="[255,255,255]" visible="true" editable="true" show-border="true" scroll-down="false" autofit="false" minimum-pixel-width="0" minimum-pixel-height="0" expression="&lt;math xmlns='http://www.w3.org/1998/Math/MathML'&gt;&lt;mstyle fontfamily='Times New Roman' mathsize='12pt' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.7099999785423279' scriptminsize='8.0pt'&gt;&lt;mrow&gt;&lt;mo fontweight='normal' lspace='0.2222222em' rspace='0.2222222em'&gt;&amp;minus;&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn fontweight='normal'&gt;216&lt;/mn&gt;&lt;mo fontweight='normal' lspace='0.0em' rspace='0.0em'&gt;&amp;InvisibleTimes;&lt;/mo&gt;&lt;mi fontweight='normal'&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mn fontweight='normal'&gt;42659&lt;/mn&gt;&lt;mo fontweight='normal' lspace='0.0em' rspace='0.0em'&gt;&amp;InvisibleTimes;&lt;/mo&gt;&lt;mi fontweight='normal'&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mo fontweight='normal' lspace='0.2222222em' rspace='0.2222222em'&gt;&amp;minus;&lt;/mo&gt;&lt;mn fontweight='normal'&gt;42875&lt;/mn&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/mstyle&gt;&lt;/math&gt;"></EC-MathContainer></Font></Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"></Text-field>
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</Section></Table-Cell></Table-Row></Table>
</Section>
</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="100%" captionalignment="0" showinput="true" captionposition="1" id="Table17" alignment="left" randomized="false" labelreference="L169096" 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">
<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field bookmark="E" style="Heading 1" foreground="[153,51,102]" layout="Heading 1" alignment="centred"><Font foreground="[153,51,102]">Extra</Font></Text-field></Title>
<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 2" layout="Heading 2"><Font size="12" foreground="[153,51,102]">Ex E1 : Tempo de espera para um segundo sucesso</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" width="1084.9624" captionalignment="0" showinput="true" captionposition="1" id="Table18" alignment="left" randomized="false" labelreference="L188873" showgroup="true" order="row"><Table-Column weight="1443" 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"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L189343" drawlabel="true">
<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 um n\303\272mero indeterminado de vezes independentemente.</Font></Text-field>
</Input>
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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"></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> obtenha o segundo FACE no segundo, terceiro e quarto arremessos.
(ii) Pr para obter o segundo FACE em </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjJGNS9GOVEnbm9ybWFsRic=</Equation><Font foreground="[153,51,102]" encoding="UTF-8">-\303\251simo lance para </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2L1EvJkdyZWF0ZXJFcXVhbDtGJ0YyRjUvRjlRJ25vcm1hbEYnLyUmZmVuY2VHRjcvJSpzZXBhcmF0b3JHRjcvJSlzdHJldGNoeUdGNy8lKnN5bW1ldHJpY0dGNy8lKGxhcmdlb3BHRjcvJS5tb3ZhYmxlbGltaXRzR0Y3LyUnYWNjZW50R0Y3LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUS1JI21uR0YkNiZRIjJGJ0YyRjVGP0YyRjVGPw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2L1EvJkdyZWF0ZXJFcXVhbDtGJ0YyRjUvRjlRJ25vcm1hbEYnLyUmZmVuY2VHRjcvJSpzZXBhcmF0b3JHRjcvJSlzdHJldGNoeUdGNy8lKnN5bW1ldHJpY0dGNy8lKGxhcmdlb3BHRjcvJS5tb3ZhYmxlbGltaXRzR0Y3LyUnYWNjZW50R0Y3LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUS1JI21uR0YkNiZRIjJGJ0YyRjVGP0YyRjVGPw==</Equation><Font foreground="[153,51,102]">.</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">O universo adaptado ao problema \303\251 o conjunto \316\251 dos seguintes </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]"> </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]">(i) </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]">.</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">(ii) O local do segundo FACE est\303\241 na linha </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEibkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEibkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> , portanto, resta apenas colocar o primeiro FACE antes. H\303\241 sim </Font><Equation executable="false" style="2D Math" input-equation="" 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size="10" foreground="[0,51,0]" encoding="UTF-8"> lugares poss\303\255veis para este : </Font><Equation executable="false" style="2D Math" input-equation="" 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size="10" foreground="[0,51,0]" encoding="UTF-8"> , \342\213\257\342\213\257 , </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">Cada uma das seq\303\274\303\252ncias acima tem a mesma 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"> ent\303\243o</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">Tr\303\252s pessoas A, B, C se revezam jogando uma moeda equiprob\303\241vel: a primeira a rolar TACK vence. Suponha que A toque primeiro, seguido de B e C.

Calcule a probabilidade de ganhar para cada um dos jogadores.</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">O universo adaptado ao problema \303\251 o conjunto \316\251 dos seguintes </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]"> </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]">Se notarmos </Font><Equation executable="false" style="Text" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2KFEnJiM5Njk7RicvJSVzaXplR1EjMTBGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdRJXRydWVGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2KC1GLzYnUSJuRidGMi9GNkY9RjgvRj9RJ2l0YWxpY0YnRjJGRkY4LyUscGxhY2Vob2xkZXJHRj1GRy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRjJGOEY+">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2KFEnJiM5Njk7RicvJSVzaXplR1EjMTBGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdRJXRydWVGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2KC1GLzYnUSJuRidGMi9GNkY9RjgvRj9RJ2l0YWxpY0YnRjJGRkY4LyUscGxhY2Vob2xkZXJHRj1GRy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRjJGOEY+</Equation><Font size="10" foreground="[0,51,0]" encoding="UTF-8"> a continua\303\247\303\243o &quot;a primeira PILE est\303\241 na fila </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEibkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEibkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0YvRjVGOC9GPFEnbm9ybWFsRic=</Equation><Font size="10" foreground="[0,51,0]"> &quot; 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<Input><Text-field style="Text" foreground="[0,51,0]" size="10" layout="Normal"><Font size="10" foreground="[0,51,0]">O evento </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 vit\303\263rias &quot;\303\251 o conjunto  </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]"> , de probabilidade</Font></Text-field>
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size="10" foreground="[0,51,0]" encoding="UTF-8"> ent\303\243o independ\303\252ncia \303\251 equivalente a equipropabilidade em </Font><Equation executable="false" style="Text" input-equation="" 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size="10" foreground="[0,51,0]" encoding="UTF-8"> , mas isso ser\303\241 destru\303\255do se restringirmos o universo a uma parte do </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]">Por exemplo eventos </Font><Equation executable="false" style="2D Math" input-equation="" 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<Input><Text-field style="Text" foreground="[153,51,102]" layout="Normal"><Font foreground="[153,51,102]" encoding="UTF-8">Escolhe-se aleatoriamente (equiprobabilidade) uma urna e extrai-se duas bolas com reposi\303\247\303\243o: nota-se I e II os eventos &quot;escolha a urna I&quot; e &quot;escolha a urna II&quot; , </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNigtSSNtbkdGJDYmUSIxRidGNUY4L0Y8USdub3JtYWxGJ0YyRjVGOC8lLHBsYWNlaG9sZGVyR0Y0RjsvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y1RjhGRA==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNigtSSNtbkdGJDYmUSIxRidGNUY4L0Y8USdub3JtYWxGJ0YyRjVGOC8lLHBsYWNlaG9sZGVyR0Y0RjsvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y1RjhGRA==</Equation><Font foreground="[153,51,102]"> e </Font><Equation executable="false" style="Text" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYnLUkjbW5HRiQ2JVEiMkYnRjUvRjlRJ25vcm1hbEYnRjJGNS8lLHBsYWNlaG9sZGVyR0Y0RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y1RkE=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLVsxNTMsNTEsMTAyXUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYnLUkjbW5HRiQ2JVEiMkYnRjUvRjlRJ25vcm1hbEYnRjJGNS8lLHBsYWNlaG9sZGVyR0Y0RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y1RkE=</Equation><Font foreground="[153,51,102]" encoding="UTF-8">os eventos &quot;a primeira bola \303\251 vermelha&quot; e &quot;a segunda bola \303\251 vermelha&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]">o mesmo para  </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2KlEjcHJGJy8lJXNpemVHUSMxMEYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHRjcvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRj8tSSVtcm93R0YkNictRiw2KFEjSUlGJ0YvL0Y2RjRGOEY7L0Y+USdpdGFsaWNGJ0YvRjhGOy9GPlEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw==">LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2KlEjcHJGJy8lJXNpemVHUSMxMEYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lK2V4ZWN1dGFibGVHRjcvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRj8tSSVtcm93R0YkNictRiw2KFEjSUlGJ0YvL0Y2RjRGOEY7L0Y+USdpdGFsaWNGJ0YvRjhGOy9GPlEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw==</Equation><Font size="10" foreground="[0,51,0]"> , substituindo </Font><Equation executable="false" style="Text" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EicEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2KC1JI21uR0YkNiZRIjFGJ0YyRjgvRjxRJ25vcm1hbEYnRjJGNUY4LyUscGxhY2Vob2xkZXJHRjdGOy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRjJGOEZE">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EicEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2KC1JI21uR0YkNiZRIjFGJ0YyRjgvRjxRJ25vcm1hbEYnRjJGNUY4LyUscGxhY2Vob2xkZXJHRjdGOy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRjJGOEZE</Equation><Font size="10" foreground="[0,51,0]"> de </Font><Equation executable="false" style="Text" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EicEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2KC1JI21uR0YkNiZRIjJGJ0YyRjgvRjxRJ25vcm1hbEYnRjJGNUY4LyUscGxhY2Vob2xkZXJHRjdGOy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRjJGOEZE">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EicEYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EpWzAsNTEsMF1GJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2KC1JI21uR0YkNiZRIjJGJ0YyRjgvRjxRJ25vcm1hbEYnRjJGNUY4LyUscGxhY2Vob2xkZXJHRjdGOy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRjJGOEZE</Equation><Font size="10" foreground="[0,51,0]"> .</Font></Text-field>
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