You’re correct, but I still don’t find the scenario I am describing intuitive by my system 1. If I think about it (especially now that I have analyzed the problem rigorously), yes, I’ll feel that the probability should increase (though of course, with nowhere near the precision of the Bayes rule), but if you just asked me this problem yesterday, and I wasn’t watching for trap questions, I’d give you a wrong answer.
I just found Wikipedia has a whole page on this, named the girl and boy paradox. They cover lots of details there.
You’re correct, but I still don’t find the scenario I am describing intuitive by my system 1. If I think about it (especially now that I have analyzed the problem rigorously), yes, I’ll feel that the probability should increase (though of course, with nowhere near the precision of the Bayes rule), but if you just asked me this problem yesterday, and I wasn’t watching for trap questions, I’d give you a wrong answer.
I just found Wikipedia has a whole page on this, named the girl and boy paradox. They cover lots of details there.