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Probability
The Monty Hall problem
Steve Selvin, in a 1975 letter to The American Statistician; made famous by Marilyn vos Savant's Parade column of September 1990.
You are on a game show. In front of you are three closed doors. Behind one is a car; behind each of the other two is a goat. You pick door 1. The host, who knows where the car is, opens door 3 and shows you a goat. He always opens a door you did not pick, always one with a goat behind it, and if both of the other doors hide goats he picks one of them at random.
He now offers you a choice. You can stay with door 1, or switch to door 2. Only then will your door be opened. Do you stick, do you switch, or does it make no difference?