a) Box I contains 3 red and 2 blue marbles while Box II contains 2 red and 8 blue marbles. A fair coin is tossed. If the coin turns up heads, a marble is chosen from Box I; if it turns up tails, a marble is chosen from Box II. Find the probability a red marble is chosen
(b) Suppose that the one who tosses the coin does not reveal whether it has turned up heads or tails, and hence the box from which the marble was chosen is not revealed. Instead, the person reveals that a red marble was chosen. What is the probability Box I was chosen?