Correct: You should switch!
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If contestants switch every time, one of two things happens:
- With probability 2/3, the contestant's initial choice was a wrong door. In this case, the host reveals the other wrong door, and the contestant switches to the door hiding the car. Success!
- With probability 1/3, the contestant's initial choice was the door leading to the car. In this case, the host reveals one wrong door, and the contestant switches to the other wrong door.
So, with probability 2/3, the "switch" strategy will win you a car.
This is one of the most famous (and contentious) probability problems of the past ten years. If you're curious, here is more information.
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