The Monty Hall problem.
You are on a game show. There are three doors. One has a prize, the other two have goats You choose door #2. The host, who knows the answer, opens door #3 and reveals a goat. He then gives you the option to stay with your door or choose door #1. Is there any advantage to changing to the other door?

The answer is yes. Contestants who switch doors have a 66% chance of winning.

There was actually a bit of controversy surrounding the answer. It discussed in a column by Marilyn vos Savant back in 1990. After she published her answer, she reported 10,000 angry letters complaining about the answer, including from math professors. You can read more about that here: Behind Monty Hall's Doors: Puzzle, Debate and Answer?