Urn A contains six white balls and three black balls. Urn B contains seven white balls and five black balls. A ball is drawn from Urn A and then transferred to Urn B. A ball is then drawn from Urn B. What is the probability that the transferred ball was white given that the second ball drawn was white?
2 initial cases:
case 1, the ball drawn from urn A to B is W
urn B now has 8W and 5B
prob (W and W)
= prob(W from A AND W from B)
= (6/9)(8/13) = 48/117
rest of problem to check my answer:
prob(W and B) = (6/9)(5/13) = 30/117
case2: the ball from urn A to urn B is B
Prob(B and W)
= (3/9)(7/13) = 21/117
prob(B and B) = 18/117
sum of the 4 possibilities should be 1
48/117 = 30/117 + 21/117 + 18/117
= 117/117
= 1
looks good to me