🚪 The Monty Hall Problem Simulator

Test your intuition against probability!

What is the Monty Hall Problem?

Imagine you're on a game show with three doors. Behind one door is a car (🚗), and behind the other two are goats (🐐). You pick a door, then the host (who knows what's behind each door) opens one of the other doors to reveal a goat. Now you have a choice: stick with your original door or switch to the remaining unopened door.

The surprising truth: You should always switch! Switching gives you a 2/3 chance of winning the car, while staying only gives you 1/3.

The Mathematics Behind It

Initial probabilities:

After the host reveals a goat:

Therefore, switching wins 2/3 of the time, while staying wins only 1/3 of the time.

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