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?

Theorem - Horses have an infinite number of legs!
Proof - A horse has an even number of legs.
It has Forelegs on the front.
It has two legs behind.
Six legs is an odd number of legs for a horse to have.
The only number that is both odd and even is infinity.
Therefore, horses have an infinite number of legs! QED

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