Car and key hide-and-seek
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In a room are three boxes that on the outside look identical. One of the boxes contains a car, one contains a key, and one contains nothing. You and a partner get to decide amongst yourselves to each point to two boxes. When you have made your decision, the boxes are opened and their contents revealed. If one of the boxes your partner is pointing to contains the car and one of the boxes you are pointing to contains the key, then you will both win. What strategy maximizes the probability of winning, and what is the probability that you will win?
There seems to be only two possibilities, one when only two boxes are selected by both of them, which will have a chance of winning = 1/3, other one in which they select one common box and the other with a fair coin toss, which would work with probability if winning = 1/2.
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