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Aug. 10th, 2009

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?


( 6 comments — Leave a comment )
Aug. 11th, 2009 03:52 am (UTC)
I say no because 50/50 odds is 50/50 odds. But then, I wouldn't be all that disappointed by a goat. They keep the yard cut nicely short, and you can cut their hair and spin it into yarn.

If Peter Segel urged me to pick door #2, on the other hand, I'd go with that because he gives hints.
Aug. 11th, 2009 01:35 pm (UTC)
HAHA! I was going to ask if this was a logic problem or a human psychology problem. Is it about odds, or is it about if the host is trying to trick you?

as you know, I would be totally happy with a goat, as well.
Aug. 11th, 2009 01:53 pm (UTC)
It's a probability problem! :)
Aug. 11th, 2009 02:31 pm (UTC)
Yes, it is to your advantage to switch...

Let's see if I can remember why. (I had this problem in a logic class years ago...)

You have a 1/3 change of picking the car and 2/3 chance of picking a goat right off the bat. If you are going by the game show rules, Monty is going to show you a goat irregardless of whatever you choose.

Example 1: You pick the car as your first choice

Door 1 = car
Door 2 = goat
Door 3 = goat

If you choose Door 1, Monty can show you either Door 2 or 3, and in either case, switching gets you a goat.

Examples 2

Door 1 = Goat
Door 2 = Car
Door 3 = Goat

If you choose Door 1, Monty can only show you Door 3. Switching gets you the car.

Example 3:

Door 1 = Goat
Door 2 = Goat
Door 3 = Car

If you choose Door 1, Monty can only show you Door 2. Switching gets you the car.

And it doesn't matter if you pick Door 1, 2, or 3, the three outcomes are the same. So in two of the three situations, switching will get you a car.

I feel like I'm missing some details to this though... oh college, where did you go?
Aug. 11th, 2009 02:42 pm (UTC)
*always* switch. ... the reasons have already been given.
Aug. 11th, 2009 04:37 pm (UTC)
( 6 comments — Leave a comment )