These two statements sound similar, but they condition on information in different ways. That changes the sample space — and the answer.
We are told a fact about the family: at least one child is a boy.
The original four equally likely families are BB, BG, GB, and GG. The condition “at least one is a boy” removes only GG, leaving three equally likely possibilities: BB, BG, and GB.
In Part A, conditioning works like a filter: eliminate impossible cases, then treat the remaining valid families equally.
“At least one child is a boy” removes the family GG and keeps the rest equally likely.
So the answer is 1 out of 3.
“You see a boy” does not just filter — it weights families by how likely they are to produce that observation.
Total weight = 2, and BB contributes 1 of those 2.