"I have two children, and the gender of one of them is #{my_first_child.gender}." Are they not the same because of FIRST_child (which would be true), or is the FIRST just an accident here? I for one don't see how the original statement could be interpreted as describing the second algorithm. We clearly get the information that there is a girl among the children, and nothing is said about it being the first child.

Basically we have a situation where we see a person and we know he has two children, at least one of them being a girl. If it is impossible to derive correct probabilities from that information, then probability theory is useless. There is no algorithm, it is just a situation.