The Monty Hall Solution

The answer is: It's better for the candidate to switch. If he switches, his chance of winning the sports car is 2/3 (67%), but if he sticks with his original choice, it is only 1/3 (33%).

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

With this ammunition, nobody should get into trouble any more if she has to defend the truth against the infidels...

Back to the problem description

  Frederik Ramm, 2001-04-26