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He does kind of improve on it. You do have information about whether the host knows which door the car is behind. If the host does not know which door the car i
by benmmurphy 11y ago
He does kind of improve on it. You do have information about whether the host knows which door the car is behind. If the host does not know which door the car is behind he just did something very unlikely so you should update your model based on this information. Assuming you have reasonable priors about the distribution of whether the host has information about the car then after he did what he did it is very likely he has information about where the car is.
Though actually I don't think you can then use this information to answer the question because it is tainted with the assumption that the car is not behind your door. :(
- purplelobster 11y agoYes, but that's not what this problem is about. Monty Hall actually knew where the car was and never picked it, that's how the show worked. The problem is that whenever the Monty Hall problem comes up, this is never clear in the phrasing. For someone who have never seen "Let's make a deal", this is not obvious, and thus people are confounded by the problem when really it's not very confounding if you knew the facts. On a side note, I think what you talked about would be 0.2% chance: product((n-1)/n) n=3 to 1000 I'm not a stats/probability wiz, but I suppose if you need to decide between Monty Hall using his knowledge or not, you'd be fairly certain by this point...