The Monty Hall puzzle

There is a game show in which you have a choice of one of three doors. Behind two of the doors are goats, whereas the third hides a free car.

The MC asks you to pick a door and you do so, say it is door number one. The MC, who knows where the car is, then opens another door, behind which there is a goat.

You now have the choice of switching from your original selection of door #1 or changing your choice to the other unopened door.

The question is: are you better off changing to the third door or does it not make any difference?

It should be added that the MC knows where the car is, and that he is not malicious, ie it is not the case that he opens a door only if your initial guess was correct. He always opens a door that reveals a goat regardless of whether your guess is correct or not. You may also assume that it is more desirable to obtain a car than a goat.

This puzzle originates from Monty Hall's game show "Let's Make A Deal". (Stand up all you couch spuds, if you can.) It was solved in 1990 by a formidable lady yclept Marilyn vos Savant, who reportedly has the highest IQ ever measured (228).

I found the puzzle on page 233 of "The Man Who Loved Only Numbers" by Paul Hoffman. It is a biography of the legendary and oddball mathematician Paul Erdos, who in spite of probably being a genius, failed to solve the puzzle. Even after seeing the solution he still couldn't understand it. Erdos was the most prolific mathematician in history.

BTW the book is interesting, but not as good as "Fermat's Last Theorem", which covers a lot of similar ground, despite the ostensible difference of subject matter.

Solution


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