Monty Fall, the host who opens a door by accident
Three doors, one car, two goats. You pick door 1. The host stumbles and accidentally knocks open one of the other two doors, chosen entirely at random, and it happens to reveal a goat. He offers you the chance to switch to the remaining closed door.
In the classic version, where the host deliberately opens a goat door, switching wins 2/3 of the time.
In this accidental version, what is the probability of winning if you switch? Explain the difference.
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List the equally likely situations before the accident: where the car is (3 options) and which door the host knocks open (2 options). Then discard the situations that did not happen, namely those where the opened door showed the car.
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