Rework problem 7 from section 3.4 of your text, involving the selection of a colored ball from one of three bowls. Assume that you randomly pick one of the bowls: X, Y, or Z. You then randomly draw one ball out of the selected bowl and note its color. The bowls contain the following colored balls:

Bowl X: 2 red, 1 white, and 1 blue. Bowl Y: 3 red, 1 white, and 2 blue. Bowl Z: 2 red, 3 white, and 2 blue.

(1) If the ball is blue, what is the probability that it was drawn from bowl X?

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(2) If the ball is either blue or white, what is the probability that it was drawn from bowl Y?

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