The Monty Hall Problem

The Problem: Imagine that you are on a game show (like, Let's Make a Deal, for example), and you are asked to choose one of three doors. Behind one of the doors is a million dollars, and behind each of the other two is a donkey. After you choose a door, the host (just like Monty Hall), opens one of the other two doors, revealing a donkey. This is not by chance. The host knows where the money is, and will always open a door that leads to a donkey at this point.

Now the host gives you a chance to change your mind. You can switch to the unopended door or stick with your first choice. Should you switch or not? Think about it, then test your answer with the Java applet simulation.