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{SECT 0 {PARA 18 "" 0 "" {TEXT -1 0 "" }{TEXT -1 22 "Answers to worksh
eet 1" }}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "Problem 1" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "#P(ahit)=1-P(nohit)= 1-(1-.3)^4\np \+
:= 0.3;\nq  := 1-p;\nP[ahit] := 1-(q)^4;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"pG$\"\"$!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"qG$\"\"
(!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"PG6#%%ahitG$\"%*f(!\"%
" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "Problem 2" }}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 119 "#use binomail probabilities\np := 0.3;\nq \+
:= 1-p;\nfor j from 0 to 4 do \n  P[hits||j] := binomial(4,j)*p^j*q^(4
-j);\n  od; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG$\"\"$!\"\"" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"qG$\"\"(!\"\"" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>&%\"PG6#%&hits0G$\"%,C!\"%" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>&%\"PG6#%&hits1G$\"%;T!\"%" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>&%\"PG6#%&hits2G$\"%YE!\"%" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>&%\"PG6#%&hits3G$\"$c(!\"%" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>&%\"PG6#%&hits4G$\"#\")!\"%" }}}}{SECT 1 {PARA 3 "" 0 
"" {TEXT -1 12 "Problem 3 &4" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
88 "#Assuming 4 at bats per game we get\nP[streak10] = P[ahit]^10;\nP[
streak20] = P[ahit]^20;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%\"PG6#
%)streak10G$\"+v[V?k!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%\"PG6#%)
streak20G$\"+)R)>AT!#7" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "Proble
m 5" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "p := 0.35;\nq := 1-p;
\nP[ahit] := 1-(q)^4;\nP[streak10] = P[ahit]^10;\nP[streak20] = P[ahit
]^20;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG$\"#N!\"#" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"qG$\"#l!\"#" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>&%\"PG6#%%ahitG$\")v$\\@)!\")" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/&%\"PG6#%)streak10G$\"+KZs*R\"!#5" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/&%\"PG6#%)streak20G$\"+D$H#f>!#6" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "Prob
lem 6" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 138 "pA := 0.5;  #proba
bility of team A winning\npB := 1-pA; #probability of team B winning \+
\n#assume that  A is leading 3-2\nP[win] := pA +pB*pA;" }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#pAG$\"\"
&!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#pBG$\"\"&!\"\"" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>&%\"PG6#%$winG$\"#v!\"#" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "Pr
oblem 7" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "P[sweep] := pA*pA
*pA*pA;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"PG6#%&sweepG$\"$D'!\"%
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "
" 0 "" {TEXT -1 9 "Problem 8" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
253 "P[games4] := pA^4+pB^4;\nP[games5] := binomial(4,1)*pA^4*pB+binom
ial(4,1)*pA*pB^4;\nP[games6] := binomial(5,2)*pA^4*pB^2+binomial(5,2)*
pA^2*pB^4;\nP[games7] := binomial(6,3)*pA^4*pB^3+binomial(6,3)*pA^3*pB
^4;\nP[games4]+P[games5]+P[games6]+P[games7]; #check" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>&%\"PG6#%'games4G$\"%]7!\"%" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>&%\"PG6#%'games5G$\"&+]#!\"&" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>&%\"PG6#%'games6G$\"'+DJ!\"'" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>&%\"PG6#%'games7G$\"(+]7$!\"(" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\")+++5!\"(" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "P
roblem 9" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 199 "# suppose that \+
A is leading\nP[games4] := pA^3;\nP[games5] := binomial(3,1)*pA^3*pB;
\nP[games6] := binomial(4,2)*pA^3*pB^2;\nP[games7] := binomial(5,3)*pA
^3*pB^3;\nP[games4]+P[games5]+P[games6]+P[games7];" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"PG6#%'games
4G$\"$D\"!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"PG6#%'games5G$\"
%v=!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"PG6#%'games6G$\"&](=!
\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"PG6#%'games7G$\"']i:!\"'" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"']il!\"'" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}}}{MARK "2 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 
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