The Monty Hall problem
Pick a door. The host, who knows where the car is, opens another door with a goat behind it. Do you stick with your door, or do you switch?
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Try the experiment: your result will appear here, next to what most people do.
What just happened (read it after the experiment)
What most people do: The vast majority of people stick with their first door.
Switching doors wins two times out of three. With your first pick, you have a one-in-three chance of holding the car, and a two-in-three chance of being wrong. And when you’re wrong, the host has no choice but to leave the car behind the other closed door.
In 1990, Marilyn vos Savant published this answer in a magazine. She received some 10,000 letters of protest, nearly a thousand of them signed by PhDs. The great mathematician Paul Erdős himself was only convinced after seeing a computer simulation.
Our intuition about probability is wrong with remarkable confidence.
More experiments
Sources
- Marilyn vos Savant, Parade, 1990.
- Donald Granberg and Thad Brown, “The Monty Hall dilemma,” Personality and Social Psychology Bulletin, 1995.