| Imagine the host doesn't know. If you guess right, he opens a door with a goat behind it and you find yourself in the classic situation. But if you guess wrong, there's a 50% chance that the host reveals a car by accident. So the probablities look like: 33%: you guess right, the host reveals a goat
33%: you guess wrong, the host reveals a goat
33%: you guess wrong, the host reveals a car So, of the situations where the host reveals a goat, the car will be behind your door 50% of the time. If the host knows and avoids the goat, the probabilities look like this: 33% you were right; the host reveals a goat
33% you were wrong; the host reveals a goat behind door B
33% you were wrong; the host reveals a goat behind door C So in the situations where the host knows about and avoids the goat, 66% of them have the car behind the other door. In the case where the host doesn't know about the car, picking the car on your first choice makes it more likely for the host to reveal a goat. That's the difference. |