The Monty Hall Problem
You are at the final round in a game show. There are three doors. In one door there is a sports car. In the other two there are goats. The way this gameshow works is you choose a random door. Then, the host will open a different door - which always has a goat. After that you have the option to switch to the one remaining closed door, or stick with the one you have. What should you do to have the highest probability of getting the sports car?