Monty Hall has randomly placed a car behind one of three closed doors. There is a goat behind each of the other two doors. "First you choose a door by pointing to it," he explains. "Then I will open one of the other doors to reveal a goat. After I've shown you the goat, you can switch doors or keep your original choice, and you win whatever is behind that door you choose."
You point to Door #1. Mr. Hall opens Door #3 to show you a goat. Now there are two closed doors remaining, and you have to make your choice: Do you stick with Door #1? Or do you switch to Door #2?
Switch, because you now have a two-thirds chance of winning.
Most people believe that, because there are only two unopened doors left, the odds on each one must be 1/2. But the fact that Mr. Hall opens another door doesn't change the odds on Door #1: You had a one-third chance of being right to begin with, and you still have a one-third chance after he opens Door #3. You knew he was going to open another door and reveal a goat regardless of what was behind Door #1, so his action provides no new information about Door #1. Therefore, since the odds on Door #1 are still one-third, and the only other place the car could be is behind Door #2, the odds on Door #2 must now be two-thirds.