Suppose that there are two buckets. Bucket 1 contains 3 tennis balls and 5 ping-pong balls. Bucket 2 contains 4 tennis balls, 3 ping-pong balls, and 5 baseballs. An unfair coin will decide from which bucket we draw. Heads implies we draw from Bucket 1 and tails implies we draw from Bucket 2. The probability of a heads is and the probability of a tails is . Given that a ping-pong ball was selected what is the probability that it came from Bucket 2?