8. Parents have always wondered about the sex of a child before it is born. Suppose that the probability of having a male child was 50% _. and the sex of one child is independent of the sex of other children. (a) Determine the probability of having exactly two girls out of four children. (b) What is the probability of having four boys out of four children? 9. It is believed that approximately 75% of American youth now have insurance due to the health care law. Suppose this is true, and let X equal the number of American youth in a random sample of n = 15 with private health insurance. (a) Ho\"r is X distributed? (b) Find the probability that X is equal to 10 (c) Find the probability that X is at lease 10 (d) Find the probability that X is at most 10 (e) Give the mean, variance, and standard deviation ofX 10