The Monty Hall Problem

In Computer Science class, we are finally programming. Our latest assignment poses a deep math problem, called the Monty Hall Problem:

"For this game imagine that there are three doors. Behind one of the doors is a....1968 Dodge Dart. Behind the other two doors is...a goat. To play you choose a door which you hope has the car. Before the door is opened, the game host opens one of the remaining two doors and shows you a goat. Remember that since he is the host he knows where the car is and alwasy opens a door that has a goat. The host gives you a choice. You can stick to your original guess or you can switch.

The burning question here is "Should you switch?"

Full Text.

This problem is infinitely easier to solve when you program it. An online simulation of the Monty Hall problem can be found at Monty Hall Dilemma.

If you can solve this problem without using the online simulation or having the solution explained to you by someone else, you rule.