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Linear Programming of Door Selection

You are given the choice of three doors. Behind one is a new car and the others hide a barnyard animal for you to keep. After you choose door number one, your host (Monty) opens door three to reveal a goat. He then asks you if you would like to switch to door two. Has the probability of success gone from 1/3 to 1/2 and then should you switch?

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Yes, the probability of success has increased from 1/3 to 1/2 ...

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The solution answers the question below in great detail.