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: 1 red, 1 white, and 3 blue.

Bowl Y: 1 red, 3 white, and 3 blue.

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

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

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