Human Biology (Feb. 2009) published a study on the gender of children in two-child families. In populations where it is just as likely to have a boy as a girl, the probabilities of having two girls, two boys, or a boy and a girl are well known. Let x represent the number of boys in a two-child family.
a. List the possible ways (sample points) in which a two child family can be gender-configured. (For example, BG represents the event that the first child is a boy and the second is a girl.)
b. Assuming boys are just as likely as girls to be born, assign probabilities to the sample points in part a.
c. Use the probabilities, part a, to find the probability distribution for x.
d. The article reported on the results of the National Health Interview Survey (NHIS) of almost 43,000 two child families. The table gives the proportion of families with each gender configuration. Use this information to revise the probability distribution for x.
Gender Configuration....................................Proportion
Girl-girl (GG) ............................................... .222
Boy-girl (BG) ............................................... .259
Girl-boy (GB) ................................................254
Boy-boy (BB) ............................................... .265