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probability

Posted By: Randy
Date: Wednesday, 30 July 2008, at 2:59 p.m.

In Response To: probability (Chuck Bower)

Chuck's last question about Monty Hall brings up another interesting probability question.

Monty always used to show the contestant 3 doors, one of which had something good behind it. They would select one of the three doors (say #1). Then, Monty would reveal the crappy prize behind one of the other of the two doors (say, door #2). Then he would ask the contestant if (s)he wanted to trade their unopened door #1 for the unopened door #3. What should they have done? Isn't it a 50/50 proposition at that point?

The answer is it is not a 50/50 proposition, and the contestant should always have traded. The probability that they already had the good prize behind door #1 was 1/3 - same as it was in the original decision - and the probability that it was behind door #3 was 2/3.

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