The Monty Hall Problem
Imagine you are a guest in a TV game show. The host, a certain Mr. Monty Hall, shows you three large doors and tells you that behind one of the doors there is a car while behind the other two there are goats. You want to win the car. He asks you to choose a door. After you have made your choice, he opens another door, revealing a goat. He then asks you whether you want to stay with your initial choice, or switch to the remaining closed door. Would you switch or stay?
This is a fascinating paradox. For a good explanation of the solution, see montyhallproblem.com.