4.29 Gender in two-child families. 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, as- sign probabilities to the sample points in part a. c. Use the probabilities, part a, to find the probability dis- tribution 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

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