#hw27.txt. Katie McKeon. May 2, 2014. Help27:=proc() print(`ProbW(N,p)`): end: #ProbW(N,p) outputs a list of length N-1 of #the probability of winning N dollars #starting with i dollars with probability of winning #1 dollar p and probability of losing 1 dollar 1-p ProbW:=proc(N,p) local eq,var,f,i,var1: var:=[seq(f[i],i=1..N-1)]: eq:={seq(f[i]=p*f[i+1]+(1-p)*f[i-1],i=1..N-1)}: eq:=subs({f[0]=0,f[N]=1},eq): var1:=solve(eq,convert(var,set)): subs(var1,var): end: #DATA #p=1/2 #ProbW(100,1/2)[50]; # 1/2 #p=17/35 #evalf(ProbW(100,17/35)[50]); # 0.05427332779 #p=49/100 #evalf(ProbW(100,49/100)[50]); # 0.1191749199