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Posted by NickMcG on 21/9/2009, 11:45 pm
From:http://mathforum.org/wagon
Alice and Bob face three doors marked 1, 2, 3. Behind the doors are placed, randomly, a car, a key, and a goat. The couple wins the car if Bob finds the car and Alice finds the key.
First Bob (with Alice removed from the scene) will open a door; if the car is not behind it he can open a second door. If he fails to find the car, they lose. If he does find the car, then all doors are closed and Alice gets to open a door in the hope of finding the key and, if not, trying again with a second door.
Alice and Bob do not communicate except to make a plan beforehand. What is their best strategy?
Using the best strategy, what is the probability they win the car?
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