[bad_user]

Yes, but this is wrong ... the sex of the second child is in no way connected to the sex of the first child.

He didn't ask ... what's the sex of the second child? No ... he asked ...

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

Choosing a distribution that involves both children in this case is wrong, hence my answer that ordering doesn't matter. 33% is just wrong.

[NeilCJames]

What I wrote is not wrong unless, when you wrote: "So given 2 children, there are only 3 possibilities ... boy, boy girl, girl boy, girl" you are asserting that in the absence of any information about the sex of either child, 2 boys is a 1/3 probability, instead of (1/2)*(1/2)= 1/4.