Monty Hall Problem (mathematics)

Anyone heard of this before? It's a mathematical probability puzzle which is well known for confusing people when they are told the solution because it is completely counterintuitive.

The problem is as follows:

Quote:

"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. The car and the goats were placed randomly behind the doors before the show. The rules of the game show are as follows: After you have chosen a door, the door remains closed for the time being. The game show host, Monty Hall, who knows what is behind the doors, now has to open one of the two remaining doors, and the door he opens must have a goat behind it. If both remaining doors have goats behind them, he chooses one randomly. After Monty Hall opens a door with a goat, he will ask you to decide whether you want to stay with your first choice or to switch to the last remaining door. Imagine that you chose Door 1 and the host opens Door 3, which has a goat. He then asks you "Do you want to switch to Door Number 2?" Is it to your advantage to change your choice?

Note that the player may initially choose any of the three doors (not just Door 1), that the host opens a different door revealing a goat (not necessarily Door 3), and that he gives the player a second choice between the two remaining unopened doors. It is assumed that the player is trying to win the car."

The answer is in fact yes, you double the probability of you getting the correct door (from 1/3 to 2/3) if you switch your choice. I, like most others, initially refused to accept this and it took me a few minutes before I could see why the chances are greatly increased if you swap your choice.

I think this is rather amusing by just how many people refuse to accept the reality of the situation.