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The first time it lands heads and second time it lands

A hat contains n coins, f of which are fair, and b of which are biased to land heads with probability 2/3. A coin is drawn from the hat and tossed twice, the first time it lands heads, and the second twice. The first time it lands heads, and second time it lands tails. Given this information, what is the probability that it is a fair coin?

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Basic Statistics: The first time it lands heads and second time it lands

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Basic Statistics: The first time it lands heads and second time it lands

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