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Probability

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In a 1970’s game show, a contestant was given a choice of three doors of which one contained a prize. The other two doors contained gag gifts like a chicken or a donkey. After the contestant chose an initial door, the host of the show then revealed an empty door among the two un-chosen doors, and asks the contestant if he or she would like to switch to the other un-chosen door. The question is should the contestant switch. Does the probability of winning increase by switching to the remaining door?

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