Bag I contains 3 white objects and 4 black objects, and Bag II contains 2 white and 6 black objects.
a) You pick an object randomly from Bag I and place it into Bag II. Next you pick an object randomly from Bag II. What is the probability that the object is black?
b) This time, you pick a Bag at random, each of the two Bags being picked with probability ½, and you pick an object at random from the chosen Bag. Given the ball is black, what is the probability you picked Bag I?