There are three urns A, B and C. Urn A contains 4 white balls and 5 blue balls. Urn B contains 4 white balls and 3 blue balls. Urn C contains 2 white balls and 4 blue balls. One half is drawn from each of these urns. What is the probability that out of these three balls drawn, two are white balls and one is a blue ball?
Urn A Urn B Urn C
White 4 4 2
Blue 5 3 4
P(two white and one blue) = P(WWB) + P(WBW) + P(BWW)
= P(W) P(W) P(B) + P(W) P(B) P(W) + P(B) P(W) P(W)
