[bad_user]

You know, the problem with that conditional probability is that the sex of the second child is in no way conditioned by the sex of the first child, so ...

  p(boy = 2 | boy >= 1) = p(any child = boy)

And this was the original problem that led them to the 33% probability.

[dododo]

in the sample space i was intending, that would not be the case. i was imagining boy as a random variable that counts instances in an order tuple of genders (the underlying sample space).

you're right, without this explicit construction, it's problematic.