Switching doors after one is revealed can double your odds of winning the car
You're shown three doors. Behind one is a car, behind the other two are goats. You pick a door, then the host, who knows what's behind each one, opens a different door to reveal a goat and asks if you'd like to switch to the remaining door. Should you switch, stay, or does it not matter?
Reveal the answer
Switch: you win the car two-thirds of the time if you switch, versus one-third if you stay. Your first pick had a 1-in-3 chance of being right; the host's forced reveal of a goat doesn't change that, it just transfers the combined 2-in-3 probability of the other two doors onto the single door left unopened. The problem is named after game show host Monty Hall and became famous in 1990 when columnist Marilyn vos Savant gave this correct answer and received thousands of letters, many from mathematicians, insisting she was wrong.