Problem:
Birth order. A couple plans to have three children. There are 8 possible arrangements of girls and boys. For example, GGB means the first two children are girls and the third child is a boy. All 8 arrangements are (approximately) equally likely.
Required:
(i) Write down all 8 arrangements of the sexes of three children. What is the probability of any one of these arrangements?
(ii) Let X be the number of girls the couple has. What is the probability that X = 2?
(iii) Starting from your work in (a), find the distribution of X. That is, what values can X take, and what are the probabilities for each value?