Three doors, one car, and a host who always opens a losing door
You pick one of three doors, behind one of which is a car. The host, who knows what's behind every door, opens one of the other two doors to reveal it's empty, then offers you the chance to switch to the remaining unopened door. Should you switch, stay, or does it not matter?
Reveal the answer
Switch — it doubles your odds from 1/3 to 2/3. Your first pick had a 1/3 chance of being right and the other two doors combined had a 2/3 chance; the host's reveal doesn't change your original door's odds, it just concentrates that 2/3 chance onto the one remaining door. When columnist Marilyn vos Savant gave this answer in Parade magazine in 1990, thousands of readers, including mathematicians, wrote in insisting she was wrong.