Draft:Bpow1997-11

A gambler has in his pocket a fair coin and a two-headed coin. He pulls one of the coins at random from his pocket and, when he flips it, it shows heads. (a) What is the probability that it's the fair coin?

Suppose he flips the same coin a second time and again it shows heads. (b) Now what is the probability that it's the fair coin?

Suppose that he flips the same coin a third time and it shows tails. (c) And now what is the probability that it's the fair coin?

Problem by Alberto L Delgado, from the now extinct Bradley Problem of the Week.