15. A club basketball team will play a 60-game season. Thirty-two of these games are against class A teams and 28 are against class B teams. The outcomes of all the games are independent. The team will win each game against a class A opponent with probability .5, and it will win each game against a class B opponent with probability .7. Let X denote its total number of victories in the season.

(a) Is X a binomial random variable?

(b) Let XA and XB denote, respectively, the number of victories against class A and class B teams. What are the distributions of XA and XB?

(c) What is the relationship between XA, XB, and X ?

(d) Approximate the probability that the team wins 40 or more games.