General
The Monty Hall Problem: Switch or Stay?
A car is behind one of three doors. You pick door 1; the host (who knows) opens door 3, revealing a goat. What is the probability of winning the car if you switch to door 2?
People also ask
What is the answer to the Monty Hall problem?
You should switch. Switching gives you a 2/3 chance of winning the car, while staying leaves you with only 1/3.
Why does switching doors double your odds?
Your first pick has a 1/3 chance of being right. The host always opens a losing door he knows is wrong, which pushes the remaining 2/3 probability onto the other unopened door.
Is the Monty Hall problem really that hard?
Yes. It famously tricks people because our intuition says the odds become 1/2, but the math proves switching wins 2 out of 3 times.