Monday, 20 October 2008

The Game Show Problem

This is a problem which I have found stimulated my ideas about analysing probability.

The interesting part is justifying the decision.

Pretend you are on a gameshow. The gameshow host shows you three identical doors and tells you: "Behind one of these doors is a brand new car. If you pick the right door, the car is yours!" You think about it...and choose one of the doors. The host asks you, "Do you want to lock that in?" You reply, "Yes. Lock it in."

Then the host opens one of the two remaining doors that you did not choose. It is empty. "Phew," you thought, "I'm glad I didn't choose that one". Then comes the interesting part. The host asks you, "Do you want to change doors?"

What would you do? Why?

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