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It's also interesting to consider Marilyn's original "explanation" a little more closely. According to the seemingly authoritative source that John Denker quoted, the original question and her original answer were
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 #1, and the host, who knows what's behind the doors, opens another door, say #3, which has a goat. He says to you, "Do you want to pick door #2?" Is it to your advantage to switch your choice of doors?
Craig F. Whitaker
Columbia, Maryland
Yes; you should switch. The first door has a 1/3 chance of winning, but the second door has a 2/3 chance. Here's a good way to visualize what happened. Suppose there are a million doors, and you pick door #1. Then the host, who knows what's behind the doors and will always avoid the one with the prize, opens them all except door #777,777. You'd switch to that door pretty fast, wouldn't you?
This "visualization" may sound pretty compelling, but what if we further suppose that the prize was a billion dollars. Would you switch? Without some pretty solid additional information, I sure wouldn't.
John Mallinckrodt
Cal Poly Pomona
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