#C3a.txt, Jan. 29, 2015, Bayes's rule

Help:=proc(): print(` CP(A,B), CheckBayes(A,B),`):
print(` Post(L,M) `): end:

#CP(A,B): A and B are any sets, using the uniform
#distribution, the conditional probability that
#the element belogs to A if someone told that it
#belongs to B, Pr(A|B)=|A interset B|/|B|
CP:=proc(A,B)
nops(A intersect B)/nops(B):

end:

#Pr(B|A)=Pr(A|B)*Pr(B)/Pr(A)
CheckBayes:=proc(A,B) :
evalb(CP(B,A)=CP(A,B)*nops(B)/nops(A)):
end:

#Post(L,M): inputs a list of prob. (that add to one)
#of length m, say, describing the step-1 scenarios
#(going to city i has prob. L[i]).
#There are n secondary  destinations
#If you are already to city i your prob. if M[i][j]
Post:=proc(L,M) local i,j,tot,P,P1:

#Prob. of getting to j via i (starting at NB):
#Prob(NB->i)*Prob(i->j)

P:=[]:

for j from 1 to nops(M[1]) do


 tot:=add(L[i]*M[i][j],i=1..nops(L)):


P1:=[seq(L[i]*M[i][j]/tot,i=1..nops(L))]:

P:=[op(P), P1]:
od:
P:
end: