I find it hard to believe myself too. But I mean, maybe I don't because the way that you stated the problem, everything made the super duper perfect sense. Sometimes when people state problems like this, they kind of want people to get the wrong answer just to explain the trickiness of it. So they kind of hide that Monty Hall will only ever open a door where the car is not there. And that does change the problem. It's one thing I tell my students in a through in probability or math in general, being really clear about what you're saying is very important.

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