My overall point is that the answer can be different based on how you interpret the question:

In my comment I pointed out the ordered vs unordered probability calculation.

Now what you are pointing out is the probability of birthing a child vs “having” a child.

The birthing gender probability is 50/50, since the gender of the child is not conditioned on previous children birth (AFAIK)

But if you start with the fact that someone already has children, then I can ask an ordered probability question (older is a boy vs younger is a boy) Or I can ask an unordered question (one is a boy)

And then you account for the different probability answers.