HackiNews

• Vakaiser
  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.

  • rcxdude
    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.
• salamandars
  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?"