I disagree with Jordan Drachman’s second scenario.
You only know that one of the two children is a girl. Case 1 and case 3 are therefore identical.
Your only possible outcomes are:
male-female
male-male
female-female.
We know that the second outcome is impossible, therefore there is a 1 in 2 chance that the other child is a boy,
and a 1 in 2 chance that the other child is a girl.
I’m sure you’re right, Irishman, but the title as it is now has a zen-like simplicity that intrigued me. If our friend bugg asks for a less cryptic title I will be glad to oblige.