A three door problem

Alf appears on a game show and is shown three doors. Behind one door, he is told, is a car. behind each of the other two doors is a goat. Alf is asked to choose a door and he does so. The game show host then opens one of the remaining two doors to reveal a goat. Alf is asked whether he wants stick with his originally chosen door or switch to the other unopened door. His prize is whatever lies behind his final choice of door.
Assuming Alf wants to win the car, should he switch?

Now you've gone and done it.

http://mathworld.wolfram.com/MontyHallProblem.html

Originally posted by XanthosNZ
Now you've gone and done it.

http://mathworld.wolfram.com/MontyHallProblem.html

ahhh, aware of the answer to the problem. Nevermind. 😛

EDIT: As a side note, it is amazing how many people insist that it is a 50% probability no matter how much evidence is presented.

Originally posted by lausey
ahhh, aware of the answer to the problem. Nevermind. 😛

EDIT: As a side note, it is amazing how many people insist that it is a 50% probability no matter how much evidence is presented.

It's extremely counterintuitive when you first think about it. Everyone is so careful not to fall for the Gambler's Fallacy that they straight away assume that's the "trick" to the question.

Not again 😞


Additional: This puzzle stumped even the great mathematician Paul Erdös.

There is actually a flaw in this puzzle mentioned here. It does not mention if the host knew where the car was or not. If he knew and delibrately picked a door which has a goat, then it would be 2/3 probability to switch. Would be 50-50 if the host did not know and happened to pick a door with a goat.

Originally posted by lausey
There is actually a flaw in this puzzle mentioned here. It does not mention if the host knew where the car was or not. If he knew and delibrately picked a door which has a goat, then it would be 2/3 probability to switch. Would be 50-50 if the host did not know and happened to pick a door with a goat.

wouldn't make for good tv if the host revealed where the car was....do you want to switch to the door that i've just shown you has the car behind it?....."hmm, that's a tough one Monty"

Originally posted by uzless
wouldn't make for good tv if the host revealed where the car was....do you want to switch to the door that i've just shown you has the car behind it?....."hmm, that's a tough one Monty"

Depends if you want a male or female goat.

Originally posted by uzless
wouldn't make for good tv if the host revealed where the car was....do you want to switch to the door that i've just shown you has the car behind it?....."hmm, that's a tough one Monty"

I don't see why anyone would change their choice. Either you get a car, which is more than you'd expect to get from a game like this, or you get a goat, which is the best thing in the world.

Originally posted by AThousandYoung
I don't see why anyone would change their choice. Either you get a car, which is more than you'd expect to get from a game like this, or you get a goat, which is the best thing in the world.

I think the rule is that you can take the car or the car's value in goats. Therefore the true goat lover would also want to get the car, so that it can be converted into a whole herd of goats for personal enjoyment.