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That's the whole reason why the problem is tough. It's carefully worded to be ambiguous about that point so that most people assume it was random (most of the e

by tel 11y ago

That's the whole reason why the problem is tough. It's carefully worded to be ambiguous about that point so that most people assume it was random (most of the erroneous math people pull out is valid were it random) but the problem actually makes little sense if Monty picked randomly since it completely ignores the potential possibility that he picked the car door. The problem isn't probabilistically difficult and most people's intuitions would be on point if it weren't set up to deceive.

JoeAltmaier 11y ago
Ah. In my generation, who actually watched the program, there is no ambiguity. No intent to deceive was detected by me. Its not supposed to be a trick question. Its supposed to illustrate how far off our intuition is about statistical behavior. Monty himself mentions that he would occasionally try hard to argue contestants into swapping. They would always refuse. He would even explain that 'his door' had the better chance - nobody would listen. But I suppose that's confounded by the suspicion that he was trying to trick them.
- proksoup 11y ago
  I agree it would help to see the problem in action. Again, the part I missed was "it would be silly for him to reveal a car". I get that now, but that was not something that I intuited, and so the omission of that information I will continue to argue is at least a little bit deceptive. Even if only to those like myself who have not seen the program.
- deleted 11y ago
  [deleted]
- tel 11y ago
  This may be very true and I think that if you're more familiar with the program and recognize that the host must know the answer then it becomes more a question of statistical intuition. I'm confident that there are lots of people who still fail to make the connection (though we're getting to the point where I think people are failing less due to a lack of statistical intuition and more due to a symbolic/physical model mismatch issue), but I think this problem wouldn't be as renowned as it is if it weren't for all of the even expert statisticians who are getting fooled. In their case it's definitely a matter of them misinterpreting the situation and the way that it's worded, for someone unfamiliar with the show, is at least a little "tricky".
proksoup 11y ago
It's a trick question. That's all I want anyone to admit when they explain the answer. Thank you.
dllthomas 11y ago
The wording in the "Ask Marilyn" column appears to have been: 'Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?' Given "the host, who knows what's behind the doors", I think the original phrasing was less ambiguous than many rephrasings I encounter. It certainly could have been still clearer. Also, her answer - which was presumably read by those writing in to asset her answer was wrong - plainly states that the host always picks a losing door.

by tel 11y ago

JoeAltmaier 11y ago

Ah. In my generation, who actually watched the program, there is no ambiguity. No intent to deceive was detected by me. Its not supposed to be a trick question. Its supposed to illustrate how far off our intuition is about statistical behavior. Monty himself mentions that he would occasionally try hard to argue contestants into swapping. They would always refuse. He would even explain that 'his door' had the better chance - nobody would listen. But I suppose that's confounded by the suspicion that he was trying to trick them.

proksoup 11y ago
I agree it would help to see the problem in action. Again, the part I missed was "it would be silly for him to reveal a car". I get that now, but that was not something that I intuited, and so the omission of that information I will continue to argue is at least a little bit deceptive. Even if only to those like myself who have not seen the program.
deleted 11y ago
[deleted]
tel 11y ago
This may be very true and I think that if you're more familiar with the program and recognize that the host must know the answer then it becomes more a question of statistical intuition. I'm confident that there are lots of people who still fail to make the connection (though we're getting to the point where I think people are failing less due to a lack of statistical intuition and more due to a symbolic/physical model mismatch issue), but I think this problem wouldn't be as renowned as it is if it weren't for all of the even expert statisticians who are getting fooled. In their case it's definitely a matter of them misinterpreting the situation and the way that it's worded, for someone unfamiliar with the show, is at least a little "tricky".

proksoup 11y ago

It's a trick question. That's all I want anyone to admit when they explain the answer. Thank you.

dllthomas 11y ago

The wording in the "Ask Marilyn" column appears to have been: 'Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?' Given "the host, who knows what's behind the doors", I think the original phrasing was less ambiguous than many rephrasings I encounter. It certainly could have been still clearer. Also, her answer - which was presumably read by those writing in to asset her answer was wrong - plainly states that the host always picks a losing door.