Where is the car? (answer)

There are 3 possible outcomes, each having the probability of 1/3. Your chances of having guessed right, when you chose one of the doors, is 1/3. No mysteries here.

The probability of you having guessed wrong is 2/3. In this scenerio, owning to the action of the host (opening the door with a goat), you will win if you switch. So it is better to switch. In fact, you double your chances of winning by switching.

Statistics from the actual television show in which this game appeared bear this out. Those who found themselves in this situation and switched their choices won about twice as often as those who did not. Computer simulations also reached the same conclusion. By the way, this problem is sometimes referred to as the Monty Hall problem. You can Google it for more detailed analysis.

The Drunkard’s Walk has many of these fascinating examples of use (and misuse) of probability. Highly recommended.