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Monty Hall problem

April 19, 2008 in Interesting, but otherwise unclassifiable by markk

Imagine you are on a TV game show, asked to choose between three doors, behind which are three prizes. One of the three doors reveals a new car! The other doors, if opened, reveal goats. There is no way for you to know which is which, so you pick one at random. Without revealing what is behind the door you chose, the host (who knows which door wins the car) then opens one of the remaining doors to reveal a goat. After this, he asks if you’d like to switch your chosen door for the only other door remaining.

If you choose to switch, what are the odds that you win the car?

A one in two chance?

Nope - a two in three chance.

(If you didn’t quite follow that, the Wikipedia link above explains it much better than I did. It probably helps if you’ve actually watched that game show, too.)

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