5 ms·

The problem is in the phrasing, and you're actually not improving on it. The way you explain the problem, it would still be 50/50. What changes the situation is

The problem is in the phrasing, and you're actually not improving on it. The way you explain the problem, it would still be 50/50. What changes the situation is that the show host CANNOT open the door with the car in it. The way you phrase it, it's not clear that the show host has any information that the participant doesn't have, but he does.

tomp 11y ago
Yes, I guess making that explicit would make it even more obvious.
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 ago
  Yes, 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...

5 ms·

The problem is in the phrasing, and you're actually not improving on it. The way you explain the problem, it would still be 50/50. What changes the situation is

by purplelobster 11y ago

tomp 11y ago
Yes, I guess making that explicit would make it even more obvious.
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 ago
  Yes, 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...