Up for a probability challenge?

Today after a long time I came across an interesting probability question. I think there are two ways to solve this problem but don't know which one is correct. Leave me a comment if you know the right answer.

"A couple has two children and at least one of them is a boy. What is the probability that their other child is a boy?"

1) 1/2, it is equally likely that the other child is a boy or a girl.
2) 1/3, in terms of order of birth, there are four possibilities for the couple's children: BB, BG, GB, GG. At least one child is a boy, rules out the the possibility GG, ;leaving you with three possibilities: BB, BG, GB. With two of these, the probability of the other child being a girl is 2/3. Leaving the probability of the other child being a boy at 1/3.