Editing 1282: Monty Hall
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However, assuming that the host has knowledge of which doors contain goats, and that their choice of which door to open is always an unchosen door containing a goat, it is actually twice as likely that the contestant will win the car if they switch than if they keep their original choice. This is because the contestant initially had a one-in-three chance of choosing the car and a two-in-three chance of choosing a goat. Switching always wins the car in those two-thirds of cases where the contestant initially chose a goat. The probability of winning by switching is therefore the same as the probability that the contestant initially chose a goat. | However, assuming that the host has knowledge of which doors contain goats, and that their choice of which door to open is always an unchosen door containing a goat, it is actually twice as likely that the contestant will win the car if they switch than if they keep their original choice. This is because the contestant initially had a one-in-three chance of choosing the car and a two-in-three chance of choosing a goat. Switching always wins the car in those two-thirds of cases where the contestant initially chose a goat. The probability of winning by switching is therefore the same as the probability that the contestant initially chose a goat. |