A couple gives birth to a girl with probability $p$, a boy with probability $q=1-p$.
Let $N$ be the number of children needed so that at least both a girl and a boy are born.
What is the distribution of $N$?
For $ P(N=k), k \ge 2, $ two children should be picked such that one is girl and one is boy, so $ P(N=k)={k \choose 2} pq. $ I feel this is not correct.