Comments by "L.W. Paradis" (@l.w.paradis2108) on "The Simple Question that Stumped Everyone Except Marilyn vos Savant" video.

But this isn't hard! It's obvious.
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@RonaldABG Cool, thank you. This one has me going back and forth. The original one was easy, I thought.
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I once found an actual error in one of her columns, involving The Bookworm Problem. Let's say a book has 100 pages. If a bookworm eats through the last page of a book, it necessarily eats through the next to the last page as well; similarly for the first page. (She thought mathematically, and forgot physics.) I wrote to a journalist who had written an article about her. He said I was right, but failed to mention any correction. Figures. She's famous.
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@Hank254 But just very slowly go through the possibilities. Or look at it this way: suppose Monty doesn't know where the car is. He opens one of the two remaining doors, and we see the car. Therefore, we know the contestant lost. Now suppose Monty opens one of the two remaining doors, and we see a goat. He just eliminated one of the ways the contestant might have lost. Obviously the contestant should switch. Or, say A and B can randomly pick any one of the three doors. A picks Door One, and B has no idea that A picked Door One. Then B has a 1/3 chance of picking Door One as well. Now suppose B does not pick Door One, but picks either Door Two or Door Three -- revealing a goat. Obviously with this new information, the probability of the car being behind the door no one picked is now 2/3. It was never 1/2, because it wasn't 1/2 between Doors Two and Three when B made his choice. Is this correct, or am I loopy now as well? 🤭
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@Hank254 No, the information gleaned in my first example is exactly the same. Monty not knowing he is about to reveal a goat doesn't matter. The fact that he does reveal a goat is the additional information.
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@Hank254 The problem involves revealing a goat behind one of the doors the first contestant did NOT pick. It does not matter who reveals the goat, or whether with foreknowledge that they were about to reveal a goat. "Monty knows" simply eliminates the possibility that the car is behind one of the remaining doors and is revealed to be. Once a goat has been revealed by Monty, what does it matter whether Monty revealed it knowingly or not? This was actually a debate among savvy statisticians who agreed with Marilyn (and thus did not err in the original problem). This is the interesting problem, not the original one. I go back and forth on this one. I don't think the knowledge of the parties involved has the least bearing on the analysis. I think that's window dressing to make a plausible story.
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@Hank254 This is so interesting. When I first saw this problem, I also analyzed it as you just did. Now I wonder what made me change my mind? Cognitive question, not a mathematical one.
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@Hank254 Wait a second, though. The contestant knows nothing about whether Monty showed him the goat because he knows where the car is, or simply by chance. Or in any case, his belief that Monty knows would be, strictly speaking, conjectural. So why does it matter, from his standpoint, having in that moment to decide whether to change his answer, knowing only that he was just shown a goat behind a door he did not pick?
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@klaus7443 All right. Suppose he doesn't. (In fact, how could he, practically speaking, were this to be an actual scenario rather than a logic exercise? He can only know what he was told. Whether what he was told is true was a separate question.) How does that change the decision chart presented in the video, if at all? Notice that I am asking literal questions. I am not suggesting the chart does not change. I am asking for a chart based on the premise that the contestant does not know whether Monty chose deliberately or randomly. It may or may not be different from the decision chart provided in this video, with the given premises. I literally don't know. I do remember that it was a subject of debate among statistics professors who immediately saw the analysis when the given premises are adopted. I also remember that one side, then the other, seemed more persuasive to me, but that I never really knew the right answer.
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@klaus7443 My "problem" is that I have to think this through for myself. You've revealed nothing to me beyond restating the answer. So? Big deal.
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@klaus7443 Good question. Blocked.
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@klaus7443 BTW, I wasn't arguing. I was seeking authentic instruction. Too bad I picked up an answer from someone incompetent in that area.
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I once found an actual error in one of her columns, involving The Bookworm Problem. Let's say a book has 100 pages. If a bookworm eats through the last page of a book, it necessarily eats through the next to the last page as well; similarly for the first page and the second. They are on the same sheet, and the usual pagination and binding we find in modern books were specified in the problem. (She thought mathematically and forgot physics.) I wrote to a journalist who had written an article about her. He said I was right, but failed to mention any correction in a future article. Figures. She's famous.
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