A family has n children with probability pn, n 1, where (1 p)/p.

Question:

A family has n children with probability αpn, n ≥ 1, where α ≤ (1 − p)/p.
(a) What proportion of families has no children?
(b) If each child is equally likely to be a boy or a girl (independently of each other), what proportion of families consists of k boys (and any number of girls)?