How many boys and girls?

A family has three children. The first is a girl. You know at least one of the remaining two is a boy. Assuming there is a 50/50 probability of birthing boys versus girls provide the probability that the family has:

1. 1 boy, 2 girls
2. 2 boys, 1 girl

There is a traditional answer. Is it
(1) 2/3, (2) 1/3?
(1) 1/2, (2) 1/2?
(1) 1/3, (2) 2/3?

There is a subtle error in the phrasing of the puzzle. As a result the answer is not well determined. What is the error?
Answer