Quote:
Originally Posted by henry2015
Hi professor, with your example  having two bags one with two black balls and one with two white balls.
I thought we had:
P[first ball is black] = P[B] = 1/2
P[first ball is black and second ball is back] = P[A and B] = 1/2
P[second ball is black given first ball is back] = P[A  B]
= P[A and B] / P[B] (by Bayes' Theorem)
= 1/2 / 1/2
= 1
eshmrt said "P[AB]P[B] = 1/2" and you said the calculation is right...so I am confused.
Maybe I miss something...

I can't see the discrepancy that is confusing you. "P[AB]P[B] = 1/2" is correct because P[B]=1/2 and P[AB]=1, both of which you correctly arrived at.