There are three types of coins which are indistinguishable apart from their probability of landing heads when tossed.
- Type A coins are fair, with probability .5 of heads
- Type B coins have probability .6 of heads
- Type C coins have probability .9 of heads
You have a drawer containing 4 coins: 2 of type A, 1 of type B, and 1 of type C. You reach into the drawer and pick a coin at random. Assuming the first two tosses were heads, what is the posterior predictive probability of heads on the third toss?
(the answer is 0.71522 but I can't figure out how)