Monty Hall Problem

Read the following problem and think of your answer before reading the rest of this post.

“Suppose you’re on a game show, and you’re given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what’s behind the doors, opens another door, say #3, which has a goat. He says to you, “Do you want to pick door #2?” Is it to your advantage to switch your choice of doors?”

Well, what do you think?  Should you switch, stay, or does it matter?

I first saw this question when I was in college.  It appeared in a 1990 Q&A feature of PARADE magazine.  Marilyn Vos Savant, the author of the feature, correctly advised that contestants should switch their choice to double their odds of winning.  She was subsequently deluged with faxes and letters (no e-mail at that time) telling her she was wrong. Some of these letters were from Ph.D.’s in mathematics.  She wrote a couple of follow-up articles, and most readers eventually seemed to be convinced that she was correct.

Link with the full original article, responses, and follow-up articles The responses  from Ph.D’s  and others (all men, BTW) who rather rudely tell her she’s wrong are hilarious.  Especially since she’s correct!

Simulation Click here to try out a simulation of the problem.

(Reposted from November 9, 2009.)

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