The Three Door Problem

So I tried to explain the three-door problem to my wife last night. The problem goes like this

"You are on a game show. The host shows you three doors. One of the doors has a fabulous prize behind it. The other two doors have booby prizes behind them. You pick a door. The host then reveals one of the other two doors as the holder of a booby prize. You are given the option of keeping your door or switching. Which should you do?"

The solution is that you should always switch. This is counter intuitive because you are looking at the two remaining doors and think "OK, now it's 50-50." But in truth its 1/3 - 2/3.

When you consider any one particular door A, you have a 1 in 3 chance of being right and a 2 in 3 chance of being wrong. By eliminating one door, the host gives you additional information, but he does not change the probability. Even if the host allowed you to pick both of the other doors you know that you would be getting at least one booby prize, but you would have a 2 in 3 chance of winning the car.

Here is a link to another explanation of the three door problem.