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Posted by NickMcG on 22/9/2009, 2:17 am, in reply to "Re: My favorite probability puzzle of all time."
Using your strategy:
Bob finds car with probability 2/3.
If Alice gets to have a turn she therefore knows car is either behind door 1 or 2. She therefore deduces that the key is behind 1,2 or 3 with probabilities .25, .25, .5 respectively.
She tries door 3 first then 1 or 2 so her probability of success is .75.
Overall, Bob and Alice win the car with probability: (Bob finds car) * ( (Alice finds key)= 2/3 * 3/ 4 = 1/2.
Tough to see how they can do better than that; but they can.
How?
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