Personally, I find that the ambiguity and phrasing of the question is what leads to pedantic 'gotchas'.
9017 children are born and 4263 are female while the remainder are male; what's the probability that the next child born is female?
It's 50%, if one assumes a bimodal distribution without atypical karyotypic deviations. Preceding births do not determine future births. They are causally independent events.
1245 of those children were born on Friday; what's the probability that the next child is male?
Still 50%. Week day of birth does not impact sex distribution.
It's the way the question is worded that splits this into an intuitive biological problem or an obtuse probability problem.
It's not necessarily ambiguity (though sometimes it is), but more just subtlety in terms of the questions that you are asking. It's important because it can matter a lot in practice that you are running the right calculations for the information you have and not introducing a bias by missing some detail.
Here's the wikipedia article for this problem: https://en.wikipedia.org/wiki/Boy_or_girl_paradox
Personally, I find that the ambiguity and phrasing of the question is what leads to pedantic 'gotchas'.
9017 children are born and 4263 are female while the remainder are male; what's the probability that the next child born is female?
It's 50%, if one assumes a bimodal distribution without atypical karyotypic deviations. Preceding births do not determine future births. They are causally independent events.
1245 of those children were born on Friday; what's the probability that the next child is male?
Still 50%. Week day of birth does not impact sex distribution.
It's the way the question is worded that splits this into an intuitive biological problem or an obtuse probability problem.
It's not necessarily ambiguity (though sometimes it is), but more just subtlety in terms of the questions that you are asking. It's important because it can matter a lot in practice that you are running the right calculations for the information you have and not introducing a bias by missing some detail.
Thank you for sharing this problem - I find the Monty Hall one pretty intuitive but this one is much twistier!
I have to say, I found your restated problem impossible to understand - I had to google the original problem, which was much more precise and clear:
"I have two children. One is a boy born on a Tuesday. What is the probability I have two boys?"