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Monty Hall problem


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A problem of decision making and probability judgement, first discussed by the US columnist Marilyn vos Savant (born 1946) in Parade magazine in September 1990, the solution to which is notoriously difficult to believe—when it was first published, thousands of people (including many university professors) wrote in refusing to accept it. In the simplest version, a game show host invites you to choose among three doors, behind just one of which is a car. After your initial choice, the host, who knows where the car is, opens one of the other doors to show that the car is not there and invites you to switch your choice to the remaining unopened door if you wish. The problem is: should you switch? Surprisingly, switching doubles your probability of winning the car from 1/3 to 2/3. The reason is that there is one chance in three that the car is behind your originally chosen door, and accepting the invitation to switch loses only if your original choice is right; if the car is not there and you switch, then the host's action will direct you to the right door, because in that case there is only one door that the host can open, and you will choose the other, where the car is. In many descriptions of the problem, there is a car behind one of the doors and a goat behind each of the others. The probabilistic phenomenon underlying the problem can be traced to Bertrand's box paradox, first discussed by the French mathematician Joseph (Louis François) Bertrand (1822–1900) on pages 3–4 of his book Calcul des Probabilités in 1889. Also called the Monty Hall dilemma. See also principle of restricted choice. [Named after the Canadian-born US entertainer Monty Hall (born 1921) who hosted the television game show Let's Make a Deal in which the problem was first noticed]

Subjects: Psychology.


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