A couple wants to have three children. Assume that the probabilities of a newborn being male or female are the same and that the gender of one child does not influence the gender of another child. (a) There are eight possible arrangements of girls and boys. All eight arrangements are equally likely. What is the sample space for having three children (gender of the first, second, and third child)? Use B for boy and G for girl. OS (1st child B or G, 2nd child B or G, 3rd child B or G} = OS (All B, two B one G, two G one B, all G} OS = (BBB, BBG, GGB, GGG, BBB, BBG, GGB, GGG} OS (BBB, BBG, BGB, BGG, GBB, GBG, GGB, GG}