The ‘Monty Hall’ Problem – Win a car not a goat

GoatA game show has three door – behind one is a car, behind the others are goats.

After picking a door the game show host says. “I’ll open one of the other doors to reveal a goat. After I’ve shown you the goat, you can stick with your initial choice, or switch to the remaining door. You win whatever is behind the door.”

What should you do?

Intuitively you might think it makes no difference – you have two doors left: a goat behind one and a car behind the other the odds of winning are the same either way… but you would be wrong. You should switch because you have a ⅔ chance of winning if you do and a ⅓ chance if you don’t.

Don’t believe me? Have a look at the decision tree below.

Monty Hall problem

You only lose if you picked the door with the car behind it initially (a 1 in 3 chance) otherwise you win by switching.

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