Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Use Bayes rule to mechanically solve probability riddles

cloud.disroot.org

Post reply on HN
Print view View original

1–10 of 45 posts

Re: Use Bayes rule to mechanically solve probability riddles

#2

Post by kgwgk »

> You're told that at least one of them is a girl.

> Likelihood of at least one girl

What the “mechanism” requires is “likelihood of being told that at least one of them is a girl”.

Use Bayes rule to correctly solve probability riddles:

https://news.ycombinator.com/item?id=45056790

    p(both are girls | you're told at least one is a girl)
       = p(you're told at least one is a girl | both are girls) * p(both are girls) / (
            p(you're told at least one is a girl | both are girls) * p(both are girls)
            +
            p(you're told at least one is a girl | they aren't both girls) * p(they aren't both girls)
        )
The solution there assumes that p(you're told at least one is a girl | both are girls) = p(you're told at least one is a girl | they aren't both girls).

Re: Use Bayes rule to mechanically solve probability riddles

#4

Post by adammarples »

kgwgk wrote: post #2

> You're told that at least one of them is a girl. > Likelihood of at least one girl What the “mechanism” requires is “likelihood of being told that at least one of them is a girl”. Use Bayes rule to correctly solve probability riddles: https://news.ycombinator.com/item?id=45056790 p(both are girls | you're told at least one is a girl) = p(you're told at least one is a girl | both are girls) * p(both are girls) / ( p…

Assuming 100% likelihood of a truth telling quiz setter, that bfomes down to population level statistics of male vs female?

Re: Use Bayes rule to mechanically solve probability riddles

#5

Post by Shorel »

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_...

Re: Use Bayes rule to mechanically solve probability riddles

#6

Post by kgwgk »

adammarples wrote: post #4
kgwgk wrote: post #2

> You're told that at least one of them is a girl. > Likelihood of at least one girl What the “mechanism” requires is “likelihood of being told that at least one of them is a girl”. Use Bayes rule to correctly solve probability riddles: https://news.ycombinator.com/item?id=45056790 p(both are girls | you're told at least one is a girl) = p(you're told at least one is a girl | both are girls) * p(both are girls) / ( p…

Assuming 100% likelihood of a truth telling quiz setter, that bfomes down to population level statistics of male vs female?

This is not about someone choosing to lie, it’s about someone choosing what true thing to say.

If “you're told that at least one of them is a girl” was intended to mean “you ask whether at least one of them is a girl and you’re told that at least one of them is a girl” it was pretty easy to make it clear.

In that case it’s straightforward that p(you're told at least one is a girl | both are girls) = p(you're told at least one is a girl | only one is a girl) = 1 (with just the mild and reasonable assumption that you’re not being lied to.)

Edit: also the reasonable assumption that your question is unrelated to the number of girls - it’s easy to imagine settings where you asked because of something which may be correlated with the number of girls.

Re: Use Bayes rule to mechanically solve probability riddles

#9

Post by zaik »

sparsely wrote: post #7

For the last one, why does the "born on a Tuesday" information change the result? I don't see how it isn't equivalent to "born on a day", since the day of the week has no connection to the rest of the scenario. I understand why "at least one boy" does matter.

If you accept the Bayes theorem, the answer is that the likelihood of "At least one boy is born on a Tuesday" is not the same for different numbers of boys. The more boys the more likely the statement is true. Therefore this information is indicative of how many boys Mrs. Chance has.
Post reply on HN