Question: Here are two routine problems about balls in urns. You are presented with two urns. Urn I contains 3 white and 4 black balls, and

Here are two routine problems about balls in urns. You are presented with two urns. Urn I contains 3 white and 4 black balls, and Urn II contains 2 white and 6 black balls.

(a) You pick a ball randomly from Urn I and place it in Urn II. Next you pick a ball randomly from Urn II. What is the probability that the ball is black?

(b) This time, you pick an urn at random, each of the two urns being picked with probability 1

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