Re:Paradoxes of Probability and Other Statistical Strangeness
by Chinjut on Tuesday June 13, 2017 @05:26PM
(#14548792)
It's not that the probability is close to 1/2 that makes it paradoxical for most people. It's that the probability differs from 1/2 at all. As in the OP of this very thread saying "Somehow knowing the day of the week the boy was born changes the result. It's completely bizarre."
Re:Paradoxes of Probability and Other Statistical Strangeness
by justinpombrio on Tuesday June 13, 2017 @05:48PM
(#14548957)
It's the fact that it differs from 2/3. If the day of the week was not mentioned the (conventional) answer is exactly 2/3. Not 1/2.
Re:Paradoxes of Probability and Other Statistical Strangeness
by Chinjut on Wednesday June 14, 2017 @12:40AM
(#14550691)
Yes, that's also "paradoxical", though probably not the paradox that would trip people up first unless they'd seen the other problem first. But, you're right that I may have misread which departure from expected answer was bugging the OP. Nonetheless, everything else I stated still holds.
This is a testable prediction. I predict that making the source of your knowledge explicit eliminates the paradox.
To me, it feels strange that "the probability that Mr. Jones has a girl given that he has a boy born on Tuesday" is ~1/2. However, it feels normal that "You ask Mr. Jones weather he has a boy born on Tuesday, and he says yes. What is the probability that he has a girl?" is ~1/2.
Do other people agree?