| Car hidden behind Door 1 | Car hidden behind Door 2 | Car hidden behind Door 3 | |
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| Player initially picks Door 1 | |||
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| Host opens either goat door | Host must open Door 3 | Host must open Door 2 | |
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| Switching loses with probability 1/6 | Switching loses with probability 1/6 | Switching wins with probability 1/3 | Switching wins with probability 1/3 |
| Switching loses with probability 1/3 | Switching wins with probability 2/3 | ||
Solution
editSay you initially pick either of the goats, the host must open the other door with a goat behind it in order to reveal a goat. So you have one door with a goat behind it and the host has opened the other door which also has a goat behind it. The remaining door therefore must have the car behind it. So if you swap, you get a car.
If you initially pick the car, it makes no difference which door the host opens, any other door has a goat behind it. so if you swap, you get a goat.
| Player has picked a goat | Player has picked a car |
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Player has picked Door 1 and the car is behind Door 2 |
| The host opens the other goat door | The host opens the either goat door |
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| Players who chose a goat and switch must get a car | Players who chose a car and switch must get a goat |
