179 Shooting free throws. In college basketball games, a player may be afforded the opportunity to shoot two consecutive foul shots (free throws).

a. Suppose a player who makes (i.e., scores on) 80% of his foul shots has been awarded two free throws. If the two throws are considered independent, what is the probability that the player makes both shots? exactly one?

neither shot?

b. Suppose a player who makes 80% of his first attempted foul shots has been awarded two free throws and the outcome on the second shot is dependent on the outcome of the first shot. In fact, if this player makes the first shot, he makes 90% of the second shots; and if he misses the first shot, he makes 70% of the second shots.

In this case, what is the probability that the player makes both shots? exactly one? neither shot?

c. In parts a and b , we considered two ways of modeling the probability that a basketball player makes two consecutive foul shots. Which model do you think gives a more realistic explanation of the outcome of shooting foul shots; that is, do you think two consecutive foul shots are independent or dependent? Explain.