From Richard Smith
York
In your article on Keith Devlin’s Goodbye, Descartes, there is a
description of a “game show” in which the contestant chooses one of three doors
(Review, 12 April, p 42).
In fact, the odds of collecting the £10 000 hidden behind one of these
three doors must be 1/2, not 1/3 or 2/3 as the article says.
This is because after the host opens one of the doors with a banana behind
it, there are now two doors unopened. One has the £10 000 behind it, the
other has a banana; therefore the chance of picking the £10 000 is 1/2.
This is true whichever door is picked.
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The “many people who refused [to pay £10 to change their choice]” were
therefore making the rational choice.
The solution in the review is actually correct—but it requires several
pages of the book to explain why. For a full explanation, go to Planet Science,
where you will find several site addresses dealing with the Monty Hall problem
and many more readers’ letters on the topic—Ed
