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Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. . The host, who knows what's behind the doors, always opens one of the other two doors that has a goat behind it (choosing at random if both do) and then always offers you the chance to switch. He opens door No. , which has a goat, and says to you, "Do you want to pick door No. ?". What is the probability that you win the car if you switch?