The father who says it snowed

Question

In a certain town it snows on one night in eight, on average. A man claims that it snowed last night. His daughters warn you that five times out of six he lies (whatever the truth, he reports it correctly with probability 1/6 and falsely with probability 5/6). What is the probability that it actually snowed last night?

Accepted Answer

One in thirty-six, about 2.8 per cent. The two stories. He said "snow". That can happen in two ways. - It snowed and he told the truth: probability 1/8 × 1/6 = 1/48. - It did not snow and he lied: probability 7/8 × 5/6 = 35/48. Compare. Given that he said "snow", the probability it really snowed is the first story's share of the total: (1/48) / (1/48 + 35/48) = 1/36. Why so low. Two factors push the same way. Snow is rare to begin with (1 in 8), and the witness is worse than useless: a man who lies five times out of six is a reliable indicator of the opposite. His saying "snow" is actually ev…

The father who says it snowed

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