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There are 4 coins in a box. Two are fair coins and the other two are both biased coins. One biased coin is such that

There are 4 coins in a box. Two are fair coins and the other two are both biased coins. One biased coin is such that P(H) = 0.7 = 1 P(T). The other biased coin is such that P(H) = 0.3 = 1 P(T).

a. One of the 4 coins is selected at random and flipped twice. What is the probability that one toss is a head and the other is tail?

b. One of the 4 coins is selected at random and flipped once. Given that the toss is a tail, what is the conditional probability that this coin is a fair coin?

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