The Monty Hall problem stumped over 1,000 PhD mathematicians

The Monty Hall problem: you choose one of three doors; behind one is a car, behind two are goats. The host (who knows what's behind each) opens a goat door you didn't choose. Should you switch? Yes — switching wins the car 2/3 of the time. When Marilyn vos Savant published this answer in Parade magazine in 1990, she received over 10,000 letters claiming she was wrong, including nearly 1,000 from people with PhDs. Several mathematics professors wrote in to say her answer was 'embarrassingly' incorrect. Simulations and conditional probability both confirm she was right.

Source: vos Savant, Parade Magazine (1990); Tierney, New York Times (1991)