
Can you solve this problem that the world famous mathematician Paul Erdos got wrong? - amichail
A thoroughly honest game-show host has placed a car behind one of three doors. There is a goat behind each of the other doors. You have no prior knowledge that allows you to distinguish among the doors. "First you point toward a door," he says. "Then I'll open one of the other doors to reveal a goat. After I've shown you the goat, you make your final choice whether to stick with your initial choice of doors, or to switch to the remaining door. You win whatever is behind the door." You begin by pointing to door number 1. The host shows you that door number 3 has a goat.<p>Do the player's chances of getting the car increase by switching to Door 2?
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cperciva
For the problem _as stated here_ ("I'll open one of the other doors to reveal
a goat") you should switch doors.

For the version of the problem where the host doesn't know where the car is
("I'll open one of the other doors, but I don't know what it will reveal"), it
makes no difference.

For the version of the problem where the host knows where the car is and only
opens another door if the car is behind the door you picked, you should
obviously never change doors.

Usually when this problem is asked, the questioner (who usually doesn't
understand the problem himself) doesn't specify which version of the problem
he's asking about -- all of the cases I know where a famous smart guy has
answered "incorrectly" come down to the problem not being described to them in
precise terms and them not making the same assumptions about the host's
behaviour as the questioner.

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codeslinger
This is the Monty Hall problem. As such, your chances do _increase_ by
switching doors. Its simple Bayesian inference.

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DanielBMarkham
You should always switch. There's a long story why.

This one drove me nuts the first time somebody told it to me. I finally
decided never to appear on Let's Make a Deal.

Dang goats.

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dood
I confess the first time I heard this (a while ago), it drove me so nuts I
ended up writing a program to confirm the solution.

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nickb
<http://en.wikipedia.org/wiki/Monty_Hall_problem>

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amichail
If you haven't seen this before, try the problem yourself. Don't look at the
solution!

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walesmd
Isn't this the concept behind "Let's Make a Deal"

If you make it to the end - do you switch or keep what the case in your hand?

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jfoutz
perhaps a spoiler.

Consider the case with 100 doors. you pick a door. the game show host opens 98
doors, all with goats. The only remaining closed doors are yours, and one
other. Do you switch?

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davidmathers
What's the source for Paul Erdos getting it wrong?

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amichail
[http://www.amazon.com/MAN-WHO-LOVED-ONLY-
NUMBERS/dp/07868840...](http://www.amazon.com/MAN-WHO-LOVED-ONLY-
NUMBERS/dp/0786884061)

