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> And I also think you're incorrect about why it's a paradox. People are just bad at understanding and estimating things in conditional probabilities. This is
by justinpombrio 9y ago
> And I also think you're incorrect about why it's a paradox. People are just bad at understanding and estimating things in conditional probabilities.
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?
- Chinjut 9y agoIt'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."
- justinpombrio 9y agoIt'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.
- Chinjut 9y agoYes, 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.