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Monty Hall Problem


Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?


Under the standard assumptions, the switching strategy has a 2/3 probability of winning the car, while the strategy of sticking with the initial choice has only a 1/3 probability.