Urn problem - conditional probability

Consider three urns, A, B, and C. Urn A contains 6 white balls and 4 black balls, urn B contains 2 white balls and 6 black balls, and urn C is empty. Two balls are drawn at random from each one of the urn A and urn B, and are placed into urn C. (4 balls are now in urn C.) Then a ball is drawn at random from urn C. What is the probability the ball drawn from urn C is black?

I've figured out that P(K\A) = 2/3 and P(K\B) = 5/6. At least I think so. But now I don't know what to do with that. (My backslashes are for vertical lines I don't know how to type that.)