Answer:
1/3
Explanation:
This answer is unintuitive, but stick with me.
If a family has 2 children, and each can be a boy (B) or a girl (G), there are 4 possible combinations:
BB BG GB GG
We know that this family doesn't have 2 girls, leaving us with 3 options:
BB BG GB
Because the order is unspecified, all 3 of these options are possible. Only one has two biys out of 3 possibilities, so it is 1/3.