🚪 The 3 Doors Problem

(Also called the monty hall problem)

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🎮 How the Game Works

Imagine you're on a game show:

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Step 1: You pick a door.

Your Pick
?
?

Step 2: The host (who knows where the car is) opens another door (that you did not pick) and shows a goat.

Your Pick
🐐
?

Step 3: You have 2 options:

Switching is always better (wonder why?)

🚪 Play the Game

Pick a door. Then click again to either stay or switch.

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Switching won't allways work (66%), but staying makes the chance of getting a car (33%) even less probable. Find out why switching is better below. ↓↓↓

🔍 All Possible Outcomes

Switching will give you a better chance of finding the car. To find out why switching is better, you need to find out all possible solutions.

Remember: the host can only open doors that have goats and you didn't choose.

To make this clear, assume you always pick Door 1. (It won't change the chance of getting the car.)

Case 1: Car is behind Door 1

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Stay → WIN | Switch → LOSE

Case 2: Car is behind Door 2

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Stay → LOSE | Switch → WIN

Case 3: Car is behind Door 3

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Stay → LOSE | Switch → WIN

📊 What Do We Learn?

👉 Switching is twice as likely to win.

🧠 Why This Happens

When you first pick a door, you only have a 1/3 chance of being correct.

That means there is a 2/3 chance the car is in the other two doors.

The host then removes one wrong door on purpose, leaving all that probability on the remaining door.

Switching = taking the 2/3 chance.