A family has 2 children. Assuming that the sex of a child is independent of another child, and that male and female children are equally likely, calculate the following probabilities.

a) What is the probability that both children are girls?

This problem follows a binomial distribution, so

P(X=2) = b(2;2, 0.5) = 0.25

P(X>=1) = b(1;2, 0.5) + b(2;2, 0.5) = 0.5b) What is the probability that at least one of the children is female ?

Essentially the problem is asking for P(a|b), where a and b are the answers for the previous two questions. Since the beginning of the problem states that a and b are independent,c) What is the probability that both children are girls if you know that there is at least one daughter?

P(a|b) = P(a) = 0.25

The answer doesn't really make intuitive sense to me, so if anyone sees a silly mistake I made somewhere, I'd appreciate you posting about it. Thanks!