Consider families with three children, and assume that all eight possible distributions as S = {BBB, BGG, GBG, GGB, GBB, BGB, BBG, GGG} Where B is for boy and G for girl, let A= event that a family has at most two boys B= event that a family has children of both genders. Are the two events A and B independent?
The two events are dependant. Because, if event A doesn't occurs, then event B can't occur; because for A to not occur, the family will have 3 boys, then that family can't have children of both genres.