The two-headed coin

Question

A drawer holds 4 coins: 3 are ordinary fair coins, and 1 is a trick coin with heads on both sides. You grab one coin at random and flip it. It comes up heads.

What is the probability that you grabbed the two-headed coin?

Accepted Answer

Count the faces you could be looking at, treating every face as equally likely once you condition on "heads showing." The three fair coins contribute 3 heads faces and 3 tails faces. The trick coin contributes 2 heads faces. Since each coin was equally likely to be grabbed and each side equally likely to land up, all 8 faces are equally likely a priori, and 5 of them are heads: - 3 heads faces from fair coins, - 2 heads faces from the trick coin. Given that a head is showing, the trick coin accounts for 2 of the 5 equally likely heads faces, so P(	ext{trick coin} \mid 	ext{heads}) = \frac{2…

The two-headed coin

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