36. Reggie Miller of the Indiana Pacers is the National Basketball Association’s best career free throw shooter, making 89% of his shots (USA Today, January 22, 2004). Assume that late in a basketball game, Reggie Miller is fouled and is awarded two shots.

a. What is the probability that he will make both shots?

b. What is the probability that he will make at least one shot?

c. What is the probability that he will miss both shots?

d. Late in a basketball game, a team often intentionally fouls an opposing player in order to stop the game clock. The usual strategy is to intentionally foul the other team’s worst free throw shooter. Assume that the Indiana Pacers’ center makes 58% of his free throw shots. Calculate the probabilities for the center as shown in parts (a), (b), and

(c), and show that intentionally fouling the Indiana Pacers’ center is a better strategy than intentionally fouling Reggie Miller.