Are and B independant Probability problem

From the set of all families with three children a family is selected at random. Let A be
the event that “the family has children of both sexes” and B be the event that “there is at
most one girl child in the family.” Are A and B independent? Answer the same question for
families with two children and families with four children. Assume that for any family size
all sex distributions have equal probabilities.

I just don't understand these kind of math at all so if you could give a long answer or explain how to do it that would be great

A: BBG BGB GBB | GGB GBG BGG P(A) = 6/8 = 3/4
B: BBG BGB GBB | BBB P(B) = 4/8 = 1/2

P(A & B) = 3/8 = P(A).P(B)
so by the statistical definition of independence, the 2 are independent

for 2 children
A: BG GB, P(A) = 2/4 = 1/2
B: BG GB BB , P(B) = 3/4

P(A & B) = 1/2, whereas P(A)·P(B) = 3/8
P(A &B) ≠ P(A)·P(B), so the 2 are *not* independent

work out similarly for 4 children

If the A is true BBG BGG then B has 50% probability of being true.

If A is not true BBB, GGG then B still has 50% probability of being true.

If B is true GBB, BBB then A has 50% probability of being true.

If B is not true GGB, GGG then A still has 50% probability of being true.

Thus P(B) is unaffected by A and p(A) is unaffected by B, thus we say they are independent.

Both are independent because it says the family has both girl and boy which could be a girl or a boy or a girl girl or a boy boy.