I think the way you stated the first problem is ambiguous; the answer could be 1/2 or 2/3. After all, maybe you only have that information because you've met just one of your neighbour's children who happens to be a boy.

The Wikipedia article does a great job of being explicit in the differences between the 1:2 and 2:3 cases.

Unfortunately articles pop up every now and then claiming 2:3 is the correct answer (since it's counterintuitive and therefore interesting), while losing the conditions necessary for 2:3 in the translation of the problem description from mathematical to plain English.