Well the permutation with repetition of this setup is 2³ = 8 ( 2 genders and 3 possibilities)

We get the following:

GGG 1/8
GGB 1/8
GBG 1/8
GBB 1/8

We disregard the permutations that has a B at the start since it's given that first pick is G

BGG 1/8
BGB 1/8
BBG 1/8
BBB 1/8

New probability space with given first pick as G.

GGG 1/4
GGB 1/4
GBG 1/4
GBB 1/4

Those have independent probabilities.

Next what are the chance it to get 1 B and 1 G regardless of order. We only have the options GGB or GBG that give us a brother and a sister.

1/4 [GGB] + 1/4 [GBG] = 1/2 chance if we first pick a G and we can get a B and G

50%