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Medium · Probability & Statistics · Quant Trader interview question · probability, conditional-probability, game-theory, monty-hall
Consider a generalized Monty Hall problem. There are $n$ doors, where $n > 2$. Behind one door is a car, and behind the remaining $n-1$ doors are goats. You initially pick a door at random. Monty Hall, who knows where the car is, then opens $n-2$ doors, each revealing a goat. He always chooses doors that you did not initially pick and that do not contain the car. You are now given the option to switch to the one remaining unopened door. What is the probability that you win the car if you switch