The Monty Hall problem
On a game show there are three doors, one hiding a car and two hiding goats. You pick a door. The host, who knows where the car is, always opens one of the other two doors to show a goat and then offers you the chance to switch to the remaining closed door. Should you switch, and what is your probability of winning the car if you do?
History and references
Solved in 1975 by Steve Selvin.
Steve Selvin posed and solved the problem in a 1975 letter to The American Statistician. It became famous in 1990 when Marilyn vos Savant answered a reader's version in Parade magazine, and about 10,000 readers, nearly 1,000 of them with PhDs, wrote in, most saying her answer was wrong. Under the standard assumptions switching wins with probability 2/3 and staying wins with probability 1/3. Your first pick is right only one time in three, and the host's choice, which never reveals the car, does not change that, so the other closed door carries the remaining 2/3. If the host behaves differently, for example by opening a door at random, the probabilities change.
References
Solutions 0
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