Quote:
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Originally Posted by Jacklad
Take Monty out of the problem and it works the way people think it should.
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You are correct that an active dealer would influence the outcome; but the problem (in it's pure form) assumes that Monty is totally honest. That is to say, he
always reveals a goat and he
always gives the remaining contestant a chance to switch to the other door. Since his prior knowledge of which door has the money doesn't change his behaviour, his presence has no effect on the outcome of the problem. If he were replaced by a set of preprinted instructions, the outcome would be the same.
My remarks in this thread apply only to the puzzle in it's pure form with a passive dealer, because that is the way it was presented in the tv show. In the real world "professor numbers" would have asked the class for a show of hands to see how many liked each door, and then called two students who had chosen a 'goat' up front. In other words he would cheat to insure the experiment coming out the way he wanted it to. But then it's no longer a real experiment.