Suppose we have three coins. One has probability 0.25 of landing heads, one has probability 0.5 of landing heads, and one has probability 0.6 of landing heads. Suppose we choose one of the coins at random and toss it.
(i) Find the probability that the coin toss shows heads. (ii) Given that the coin toss showed heads, find the probabilities that each of the three coins was the one chosen.