Three brothers and their wives decide to have children until each family has two female children. What is the pmf of X = the number of male children born to the brothers? What is E(X), and how does it compare to the expected number of male children born to each brother?

Answer Step 1 of 3 Let success is the boy Let failure is the girl Here x= the number of male children born Here P is the probability of boy=½ P=½, q=½ Step 2 of 3 Here the no. of girls=2*3=6 Let k is the no. of boys until 6th girl The total no. of babies until 6th girl = k+5 Here it is negative binomial distribution