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You pick the car with 1/3 probability and a goat with 2/3. If you picked the car and switch, you lost. If you picked a goat and switch, you win because the only
by utopcell 5y ago
You pick the car with 1/3 probability and a goat with 2/3. If you picked the car and switch, you lost. If you picked a goat and switch, you win because the only other door left has the car.
The problem is simple to reason through. The hard part is convincing yourself that you need to think through it given what seems "obviously correct".
- h0l0cube 5y agoThis is the same explanation I arrived at too. Crucial to answering the problem correctly is understanding that the host doesn't reveal a random door, but a door that you have not chosen, and also is wrong. And then the reasoning follows naturally to the correct answer. It's amazing to be so prejudiced that someone would be adamant on the incorrect answer, when it can be explained in 3 simple lemmas.