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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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