"Do You Want to Switch Doors?"
Based on the TV show "Let's Make a Deal", this puzzle counter-intuitively demonstrates probability. There are 3 doors: behind one is a car, behind two are goats. You pick a door. The host (Monty), who knows what's behind the doors, opens another door to reveal a goat. He then asks: "Do you want to switch your choice?"
Most people think the odds are 50:50 since two doors remain. However, math proves that switching doubles your chance of winning (66.6%). Initially, you have a 1/3 chance of picking the car and 2/3 chance of picking a goat. If you picked a goat (more likely), switching wins.
This problem reveals how our brains struggle with conditional probability. Even the famous mathematician Paul Erdős initially refused to believe the solution until he saw a computer simulation. Try it yourself!