At this point, large parts of my audience usually start a revolt. At least those who know a bit about statistics will say it's a clear case: After the moderator has opened one goat door, there are two doors left - one means victory, the other defeat. That's fifty-fifty, no doubt!

But that's wrong. A vague idea of an explanation is the following: In the beginning, the probability of finding the right door is 1/3. This probability "sticks" to the door the candidate selected at first, so when one of the other doors is removed from the game, the remainig probability is 2/3 in order to have all probabilities sum up to 1. (Statisticians don't like it if the sum is not 1. This means you've made a mistake.)

If that is not a sufficient explanation for you, there's still

- an intuitive explanation,
- a mathematical proof, and
- an empirical "proof" (this program requires Java).

Back to the problem description