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Markov chains and Monty Hall · Probability · Earlier days

Monty Hall: car behind door three

Three closed doors hide a car behind one door and goats behind the other two, with the car placed uniformly at random. The contestant picks door 1 without knowing where the car is. Monty, who knows where the car is, then opens one of the other two doors, always one with a goat behind it, choosing at random if he has a choice. Suppose Monty opens door 2. What is the probability that the car is behind door 3? Round to two decimal places.

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