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This Monty Hall problem was asked to Marilyn vos Savant, a woman with an extremely high IQ, who solved it correctly, and many readers of her column, including P

by Shorel 1y ago

This Monty Hall problem was asked to Marilyn vos Savant, a woman with an extremely high IQ, who solved it correctly, and many readers of her column, including PhD and mathematicians, declared her solution wrong. Then careful analysis proved her correct. https://en.wikipedia.org/wiki/Monty_Hall_problem#Savant_and_the_media_furor https://en.wikipedia.org/wiki/Monty_Hall_problem#Savant_and_...

FabHK 1y ago
To be fair, I think this problem needs to be formulated very carefully and specifically [0], because the "correct" answer is predicated on that, and many formulations one finds (including the one in her column) are not that. [0] It has to be specified that a) Monty knows what's behind which door, and b) he will on purpose always open a door such that there's a goat behind it.
- kgwgk 1y ago
  > many formulations one finds (including the one in her column) As far as I’ve been able to find the text below would be the original question (“the host, who knows what’s behind the doors, opens”) and answer (“the host, who knows what’s behind the doors and will always avoid the one with the prize, opens”). Are you referring to that? https://web.archive.org/web/20130121183432/http://marilynvossavant.com/game-show-problem/ https://web.archive.org/web/20130121183432/http://marilynvos... 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 #1, and the host, who knows what’s behind the doors, opens another door, say #3, which has a goat. He says to you, "Do you want to pick door #2?" Is it to your advantage to switch your choice of doors? [Craig F. Whitaker - Columbia, Maryland] Yes; you should switch. The first door has a 1/3 chance of winning, but the second door has a 2/3 chance. Here’s a good way to visualize what happened. Suppose there are a million doors, and you pick door #1. Then the host, who knows what’s behind the doors and will always avoid the one with the prize, opens them all except door #777,777. You’d switch to that door pretty fast, wouldn’t you?
  - FabHK 1y ago
    Yes, indeed, thanks for digging it up. You see that Marilyn's answer contains the clarified correct specification ("the host, who knows what’s behind the doors and will always avoid the one with the prize..."), but the question does not fully specify it. Thus, ignoring the clarification in the answer (which furthermore pertains to a modified problem), one could interpret the question differently: the host randomly opens a door [0], this specific day it happens to contain a goat, should you switch? And that ambiguity has given rise to so much spilled ink (and, by the way, the misconception that statistic professors don't understand probability theory). [0] Note that specifying that the host knows what's behind what door doesn't help. They could still pick a door randomly.
    - kgwgk 1y ago
      Did any of those readers of her column, including PhD and mathematicians, that declared her solution wrong do so because they objected to the clarification? (Does it make sense to declare the answer wrong ignoring the answer?)
      - FabHK 1y ago
        I think they didn't notice the significance of that clarification (which, again, was given in the context of a modified problem). Reading the exchanges again, though, I see that many respondents were not only mistaken, but also impolite or sexist in accusing Marylin of being wrong. If you specify the problem carefully, anyone with some training in probability should get the answer right. But clearly back then it was a head scratcher. I wonder whether there've been other problems like that, or we will encounter similar ones: elementary and easy to understand, yet many people get it confidently wrong, until the correct solution permeates through culture.
        kgwgk 1y ago
        > [that clarification] was given in the context of a modified problem I don’t understand what do you mean by that. The clarification was part of the original answer in the context of the original question. The clarification was stated again and again and again. If that’s a “modified problem” so be it but that was the problem being discussed with her readers.
- griffzhowl 1y ago
  > [0] It has to be specified that a) Monty knows what's behind which door, and b) he will on purpose always open a door such that there's a goat behind it. You don't need condition (a) here. It's enough to just stipulate that a door with a goat behind it will be opened, however that comes about
  - FabHK 1y ago
    Sure. It's really b) that's important (which generally requires a). What was specified in the question though was a).
actionfromafar 1y ago
A very smart person is named "savant" and "her grandmother's name was Savant; her grandfather's, vos Savant". https://en.wikipedia.org/wiki/Marilyn_vos_Savant https://en.wikipedia.org/wiki/Marilyn_vos_Savant

by Shorel 1y ago

FabHK 1y ago

To be fair, I think this problem needs to be formulated very carefully and specifically [0], because the "correct" answer is predicated on that, and many formulations one finds (including the one in her column) are not that. [0] It has to be specified that a) Monty knows what's behind which door, and b) he will on purpose always open a door such that there's a goat behind it.

kgwgk 1y ago
> many formulations one finds (including the one in her column) As far as I’ve been able to find the text below would be the original question (“the host, who knows what’s behind the doors, opens”) and answer (“the host, who knows what’s behind the doors and will always avoid the one with the prize, opens”). Are you referring to that? https://web.archive.org/web/20130121183432/http://marilynvossavant.com/game-show-problem/ https://web.archive.org/web/20130121183432/http://marilynvos... 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 #1, and the host, who knows what’s behind the doors, opens another door, say #3, which has a goat. He says to you, "Do you want to pick door #2?" Is it to your advantage to switch your choice of doors? [Craig F. Whitaker - Columbia, Maryland] Yes; you should switch. The first door has a 1/3 chance of winning, but the second door has a 2/3 chance. Here’s a good way to visualize what happened. Suppose there are a million doors, and you pick door #1. Then the host, who knows what’s behind the doors and will always avoid the one with the prize, opens them all except door #777,777. You’d switch to that door pretty fast, wouldn’t you?
- FabHK 1y ago
  Yes, indeed, thanks for digging it up. You see that Marilyn's answer contains the clarified correct specification ("the host, who knows what’s behind the doors and will always avoid the one with the prize..."), but the question does not fully specify it. Thus, ignoring the clarification in the answer (which furthermore pertains to a modified problem), one could interpret the question differently: the host randomly opens a door [0], this specific day it happens to contain a goat, should you switch? And that ambiguity has given rise to so much spilled ink (and, by the way, the misconception that statistic professors don't understand probability theory). [0] Note that specifying that the host knows what's behind what door doesn't help. They could still pick a door randomly.
  - kgwgk 1y ago
    Did any of those readers of her column, including PhD and mathematicians, that declared her solution wrong do so because they objected to the clarification? (Does it make sense to declare the answer wrong ignoring the answer?)
    - FabHK 1y ago
      I think they didn't notice the significance of that clarification (which, again, was given in the context of a modified problem). Reading the exchanges again, though, I see that many respondents were not only mistaken, but also impolite or sexist in accusing Marylin of being wrong. If you specify the problem carefully, anyone with some training in probability should get the answer right. But clearly back then it was a head scratcher. I wonder whether there've been other problems like that, or we will encounter similar ones: elementary and easy to understand, yet many people get it confidently wrong, until the correct solution permeates through culture.
      - kgwgk 1y ago
        > [that clarification] was given in the context of a modified problem I don’t understand what do you mean by that. The clarification was part of the original answer in the context of the original question. The clarification was stated again and again and again. If that’s a “modified problem” so be it but that was the problem being discussed with her readers.
griffzhowl 1y ago
> [0] It has to be specified that a) Monty knows what's behind which door, and b) he will on purpose always open a door such that there's a goat behind it. You don't need condition (a) here. It's enough to just stipulate that a door with a goat behind it will be opened, however that comes about
- FabHK 1y ago
  Sure. It's really b) that's important (which generally requires a). What was specified in the question though was a).

actionfromafar 1y ago

A very smart person is named "savant" and "her grandmother's name was Savant; her grandfather's, vos Savant". https://en.wikipedia.org/wiki/Marilyn_vos_Savant https://en.wikipedia.org/wiki/Marilyn_vos_Savant