The Monty Hall Problem

In 1990, Marilyn vos Savant published a solution to this puzzle in Parade magazine: you choose one of three doors; behind one is a car, behind two are goats. The host opens a different door revealing a goat. Should you switch? Yes — switching gives you a 2/3 chance of winning. Nearly 10,000 readers wrote in to say she was wrong, including many with PhDs in mathematics. She was right. The problem has become the most famous illustration of how badly human intuition handles conditional probability.