A gambler has a fair coin and a two-headed coin in his pocket. He randomly selects one of the coins. (a) Suppose that he flips the selected coin twice, and both show heads. Find the probability that the selected coin is the fair coin. (b) Suppose that he flips the selected coin four times, and all show heads. Find the probability that the selected coin is the fair coin.

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A: For Fair coin : P(H) = P(T) = 1/2 For Unbalanced coin : P(T¯) = 2/3 P(H¯) = 1/3

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