Tuesday, July 8, 2008
Gameshow
You are on a gameshow. The host shows you three closed doors. Behind one of the doors is $1 million. Behind the other two doors is nothing. You begin the game by choosing one of the doors. It remains closed, but the host opens one of the other two doors and shows you that there is nothing behind it. In order to maximize your chances at winning the money, is it best for you to keep the door you originally chose, switch to the other closed door, or does it not make any difference?
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ANSWER:
You always want to switch doors. The chance of you selecting the correct door the first time around is 1/3. There is a 2/3 chance you selected wrong. When the host opens the door showing there is nothing there, the other door has a 2/3 chance of being right and your door is still 1/3. A good way to understand this is by imagining there were 1,000 doors. You select one, and the host opens up 998 other doors. Is it likely that you selected the right door the first time around, or that the one remaining other door is the right door?
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