You are given two urns each containing two biased coins. The coins in urn I come up heads with probability p1, and the coins in urn II come up heads with probability p2 ≠ p1. You are given a choice of
(a) Choosing an urn at random and tossing the two coins in this urn or
(b) Choosing one coin from each urn and tossing these two coins. You win a prize if both coins turn up heads. Show that you are better off selecting choice (a).