Help with Bayes Theorem

Question

Urn A contains seven white balls and six black balls. Urn B contains five white balls and three 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? (Round your answer to three decimal places.)

Answer 1

In my opinion the best way to handle questions of this sort is to list the possible outcomes and attach probabilities to each outcome.

from urn A from urn B

w w 7/13*6/9 = 42/117

w b 7/13*3/9 = 21/117

b w 6/13*5/9 = 30/117

b b 6/13*4/9 = 24/117

Event A is white transferred (from urn A)

Event B is white drawn from urn B

P(A|B) = P(A and B)/P(B)

Event A and B is both balls W

P(A and B) = 42/117

P(B)=(42+30)/117

Therefore, P(A|B)= 42/72= 7/12