Suppose that a particular NBA player makes 90% of his free throws. Assume that late in a basketball game, this player is fouled and is awarded two free throws.
a. What is the probability that he will make both free throws?
(to 4 decimals)
b. What is the probability that he will make at least one free throw?
(to 4 decimals)
c. What is the probability that he will miss both free throws?
(to 4 decimals)
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 the team's worst free throw shooter makes 57% of his free throws. Calculate the probabilities for this player as shown in parts (a), (b), and (c), and show that intentionally fouling this player who makes 57% of his free throws is a better strategy than intentionally fouling the player who makes 90% of his free throws. Assume as in parts (a), (b), and (c) that two free throws will be awarded.
What is the probability that this player will make both throws?
(to 4 decimals)
What is the probability that will make at least one throw?
(to 4 decimals)
What is the probability that this player will miss both throws?
(to 4 decimals)