Problem Solving

Hello!

I am puzzled by the answer of a probability question which I got from one of the GMAT Prep Now videos.

Question: If a teacher randomly selects 2 students from a group of 4 boys and 4 girls, what is the probability that the selection contains at least 1 boy?

I know that there are 2 methods to solve this question:

1) P(at least 1 boy) = 1 - P(0 boys)
= 1- P(all girls)
= 1 - P(girl 1 AND girl 2)
= 1 - (4/8*3/7) = 1 - 3/14
= 11/14 [correct answer]

However, when I try to solve it using the other method (as below), I can't seem to get the same answer.

2) P(at least 1 boy) = P(1 boy or 2 boys)
= P(1 boy) + P(2 boys)
= 4/8 + (4/8*3/7)
= 1/2 + 3/14
= 10/14

I would appreciate someone pointing out to me where I went wrong. Was it a calculation mistake or a conceptual mistake?

Thank you very much!

CASE 2:

P(at least 1 boy) = P(1 boy or 2 boys)

= P(1 boy & 1 girl) + P(2 boys & no girl) = 4C1*4C1/8C2 + 4C2/8C2 = 4/7 + 3/14 = 11/14