= 27d567bc2d48d9f40e9ccc20ea370b15)
ciphergoth comments on Bayes' Theorem Illustrated (My Way) - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (191)
I always much prefer these stated as questions - you stop someone and say "Do you have exactly two children? Is at least one of them a boy born on a Tuesday?" and they say "yes". Otherwise you get into wondering what the probability they'd say such a strange thing given various family setups might be, which isn't precisely defined enough...
Very true. The article DanielVarga linked to says:
... which is just wrong: whether it is different depends on how the information was obtained. If it was:
... then there's zero new information, so the probability stays the same, 1/3rd.
(ETA: actually, to be closer to the original problem, it should be "Select one of your sons at random and tell me the day he was born", but the result is the same.)
I get that assuming that genders and days of the week are equiprobable, of all the people with exactly two children, at least one of whom is a boy born on a Tuesday, 13/27 have two boys.
True, but if you go around asking people-with-two-chidren-at-least-one-of-which-is-a-boy "Select one of your sons at random, and tell me the day of the week on which he was born", among those who answer "Tuesday", one-third will have two boys.
(for a sufficiently large set of people-with-two-chidren-at-least-one-of-which-is-a-boy who answer your question instead of giving you a weird look)
I'm just saying that the article used an imprecise formulation, that could be interpreted in different ways - especially the bit "if you supply the extra information that the boy was born on a Tuesday", which is why asking questions the way you did is better.