Editing 1282: Monty Hall
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The switch essentially gives the contestant ''both'' remaining doors instead of just the ''one'' door originally chosen. Because the host ''always'' has at least one goat available, the fact that the host reveals a goat does not provide the contestant any new information about their initially chosen door. The initial door still has a two-in-three chance of being a goat, and switching still has a two-in-three chance of winning. Opening a goat-door simply shifts all of the probability of the remaining two doors being a car to the remaining unchosen door. | The switch essentially gives the contestant ''both'' remaining doors instead of just the ''one'' door originally chosen. Because the host ''always'' has at least one goat available, the fact that the host reveals a goat does not provide the contestant any new information about their initially chosen door. The initial door still has a two-in-three chance of being a goat, and switching still has a two-in-three chance of winning. Opening a goat-door simply shifts all of the probability of the remaining two doors being a car to the remaining unchosen door. | ||
β | '''Simple explanation''' | + | '''Simple explanation''' |
Imagine there are 100 doors instead of just 2, and after you pick a door, the host opens all but one, revealing all goats. Do you switch to the remaining door or keep your initial pick? Just as there is a 2/3 chance of picking the car when switching in the 3-door scenario, there is now a 99/100 chance of picking the car when switching in the 100 door scenario. In this scenario, it becomes obvious that it is not a 50/50 chance when two doors remain. | Imagine there are 100 doors instead of just 2, and after you pick a door, the host opens all but one, revealing all goats. Do you switch to the remaining door or keep your initial pick? Just as there is a 2/3 chance of picking the car when switching in the 3-door scenario, there is now a 99/100 chance of picking the car when switching in the 100 door scenario. In this scenario, it becomes obvious that it is not a 50/50 chance when two doors remain. | ||
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There has been great debate about the precise wording of the problem, and what assumptions or rules might apply. These variants can greatly change the probabilities. | There has been great debate about the precise wording of the problem, and what assumptions or rules might apply. These variants can greatly change the probabilities. | ||