A red urn contains one white ball and one black ball. A blue urn contains one white ball and two black balls. An urn is picked randomly (with probability 1/2 for each urn), and then a ball is uniformly drawn from that urn. Let A be the event that the ball drawn is white and let B be the event that the urn picked is red. Determine
a. P(A) and P(B).
b. P(A and B).
c. P(B|A) and P(A|B).