The Monty Hall Problem
In a tv gameshow, the candidate is shown three doors. Two doors each hide a goat, while there is a new car behind the third. Of course, our candidate has no plans to start a goat-farm and would love to return home in a brand-new car.
The candidate is asked to to choose one door, and after he has made his choice, the quizmaster (who knows what is hidden behind the doors) opens one of the two other doors, which reveals a goat.
Then the quizmaster offers the candidate the option to change his mind. The question is whether it is more favourable to choose the other closed door or if it does not make any difference which of the two remaining doors is chosen.
You may perhaps think that it does not make any difference. The chance to win the car, however, turns out to be 2/3 if the candidate changes his mind. The Java applet below shows a simulation of one million shows. The simulation clearly demonstrates that it's favourable to choose the other door: in two thirds of the shows the candidate will win the desired vehicle.
Click the applet to start it (this may take a while). After a million shows the applet will stop. If you want to see another simulation, just click again.
If you wish to see the source code of the applet, just click 'source code' on the left (bottom link).