Use Bayes rule to mechanically solve probability riddles • Hacker News Board

Re: Use Bayes rule to mechanically solve probability riddles

#41

Post by taid9iK- » Thu, Sep 04, 2025, 9:35 PM UTC

michaelcampbell wrote: post #29

kgwgk wrote: post #18

Earlier quoted context omitted.

> 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://marilynvos... Suppose you’re on a…

> Suppose there are a million doors,... This is a common way to explain it, but I always found it less intuitive; not sure why. My go to thought experiment along these lines is rather this: Adjust the game to where both you and your friend are playing at the same time. You _NEVER_ switch doors, and your friend _ALWAYS_ does, when given the choice by Monty. Since you never switch, no matter what Monty does you know yo…

Oh I like that one. I am having real trouble with the commonly used explanations.

Re: Use Bayes rule to mechanically solve probability riddles

#42

Post by FabHK » Fri, Sep 05, 2025, 2:34 PM UTC

SAI_Peregrinus wrote: post #38

FabHK wrote: post #25

Earlier quoted context omitted.

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…

The original problem is the one you're thinking of as modified, since the original problem was about a real-world game show, and the rules of the real-world show in question included Monty Hall (the host) opening a door that the player hadn't picked and which did not contain the car. The problem assumed familiarity with the game show, the clarification is for people who didn't watch the show.

The modification I'm referring to is the one Marylin suggests with a million doors, with Monty opening 999,998 of.

Re: Use Bayes rule to mechanically solve probability riddles

#43

Post by FabHK » Fri, Sep 05, 2025, 2:35 PM UTC

kgwgk wrote: post #27

FabHK wrote: post #25

Earlier quoted context omitted.

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…

> [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.

The modification I'm referring to is the one Marylin suggests with a million doors, with Monty opening 999,998 of.

Re: Use Bayes rule to mechanically solve probability riddles

#44

Post by FabHK » Fri, Sep 05, 2025, 2:36 PM UTC

griffzhowl wrote: post #40

FabHK wrote: post #15

Earlier quoted context omitted.

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.

> [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

Sure. It's really b) that's important (which generally requires a). What was specified in the question though was a).

Re: Use Bayes rule to mechanically solve probability riddles

#45

Post by kgwgk » Fri, Sep 05, 2025, 6:00 PM UTC

FabHK wrote: post #43

kgwgk wrote: post #27

Earlier quoted context omitted.

> [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.

The modification I'm referring to is the one Marylin suggests with a million doors, with Monty opening 999,998 of.

Ok, so the modification was the "Here’s a good way to visualize what happened." explanation.

I would say that the whole (short) paragraph is intended to clarify why the answer to the question is "Yes; you should switch."

Maybe it was not a good way to visualize what happened after all. Experience shows that some readers were unable to understand the argument.

However, none of them complained about the explanation being wrong because those were two completely different problems (only in the second one the host will always avoid the door with the prize, apparently).