monty hall

I'm sorry to introduce an irrelevance, but I have been bewildered by an article and subsequent correspondence in the FT about probability. The original proposal was that people do not understand probability, and some panel game was introduced to support this assertion.

The scenario is a game show, in which the presenter (the eponymous Monty Hall, apparently) has three boxes, in one of which are the keys to a car. The contestant guesses which box the keys are in; if he is right, he gets the car. But after he has made his choice, the presenter opens one of the boxes which does not contain the keys, and gives the contestant the opportunity of changing his preference. The article asserted that it was always the correct choice to switch.

Much of the subsequent correspondence has produced increasingly complicated arguments in support of the contention - none that I have read has opposed it.

My own position is based not on probability theory, but simple logic.

The contestant's first choice has a one-in-three chance of being correct. When an empty box, not one which he has chosen, is opened, his choice has a remaining one-in-two chance of being correct. But opening the empty box has told him nothing about the two remaining boxes. There is thus no advantage in switching; indeed, there is no advantage in sticking or switching. Either course of action gives the same chance of success.

Does anyone disagree, and if so, why?


--
ralph
.

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