Re: monty hall


"ralph" <ralph@xxxxxxxxxxxxxxxxxxxxx> wrote in message
news:NTcj+vDyq2CDFwGQ@xxxxxxxxxxxxxxxxxxxxxxxx
> 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?
>

It is easily shown that by switching the chances of success increase two
fold. You can find the explanation in many websites -The New Scientist's
page on the Monty Hall problem is quite good, for example. If the
mathematical explanation fails to convince you just do the experiment many
times and you will see clearly how your chances increase by switching.

regards
Milan


.

Relevant Pages

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