The Monty Hall Problem

The Monty Hall Problem is named after the host of an old game show called "Lets Make a Deal". Basically, in the show, the contestant had a chance to win a car. Naturally, as with all game shows, there was a risk of winning nothing. So here is basically how the game plays.

Monty shows you three closed doors. There is a car behind one door and a goat behind the other two. If you open the door with the car, you win it. If you open a door with a goat, you don't win the car. Simple, right?

Here is where the problem part comes in. After you pick a door, but before the door is opened, Monty will open one of the doors that you didn't pick to reveal a goat (Monty knows where the car is so he always opens a door with a goat behind it). At this point, you have a choice. Do you stick with your original door or do you switch to the other unopened door?

For example, suppose you pick Door 1. Monty opens Door 3 to reveal a goat. Do you stick with Door 1 or switch to Door 2?