Suppose you have three bags containing only red marbles and blue marbles. Bag one has two red marbles and four blue marbles, bag two has eight red marbles and four blue marbles, and bag three has one red marble and three blue marbles. I pick one marble (at random) from each bag.
(a) What is the probability that I picked exactly two red marbles?
(b) Suppose I picked two red marbles but forgot which bag they came from. What is the probability that I picked a red marble from bag one?