The famous probability puzzle that fools everyone
Step 1: Pick a door (one has a car, two have goats)
Step 2: Host reveals a goat behind one of the other doors
Step 3: Do you switch to the remaining door or stay?
Surprising Answer: Always switching wins 2/3 of the time!
| Your Pick | Host Opens | Stay Result | Switch Result |
|---|---|---|---|
| Door 1 (Car) | Door 2 or 3 | WIN | LOSE |
| Door 2 (Goat) | Door 3 | LOSE | WIN |
| Door 3 (Goat) | Door 2 | LOSE | WIN |
Stay wins: 1/3 (33.3%) | Switch wins: 2/3 (66.7%)
Your initial choice has a 1/3 probability of being correct.
When the host reveals a goat, your door's probability stays at 1/3.
But the other unopened door now has a 2/3 probability!
Why? The host's action is not random - they know where the car is and deliberately avoid it. This concentrates the probability in the remaining door.