Can you solve this problem that the world famous mathematician Paul Erdos got wrong? | Hacker News Reader

Can you solve this problem that the world famous mathematician Paul Erdos got wrong?

7 pointsamichail10 comments

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.

Do the player's chances of getting the car increase by switching to Door 2?

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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.

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

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.

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.

http://en.wikipedia.org/wiki/Monty_Hall_problem

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

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?

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?

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

http://www.amazon.com/MAN-WHO-LOVED-ONLY-NUMBERS/dp/07868840...

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