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Jamal Crawford of the National Basketball Association’s Portland Trail Blazers is the best free-throw shooter on the team, making 93% of his shots (ESPN website, April 5, 2012). Assume that late in a basketball game, Jamal Crawford 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 Portland Trail Blazers’ 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 Portland Trail Blazers’ center is a better strategy than intentionally fouling Jamal Crawford. Assume as in parts (a), (b), and (c) that two shots will be awarded.

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
Chapter 4.4, Problem 36E
Textbook Problem
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Jamal Crawford of the National Basketball Association’s Portland Trail Blazers is the best free-throw shooter on the team, making 93% of his shots (ESPN website, April 5, 2012). Assume that late in a basketball game, Jamal Crawford is fouled and is awarded two shots.

  1. a. What is the probability that he will make both shots?
  2. b. What is the probability that he will make at least one shot?
  3. c. What is the probability that he will miss both shots?
  4. 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 Portland Trail Blazers’ 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 Portland Trail Blazers’ center is a better strategy than intentionally fouling Jamal Crawford. Assume as in parts (a), (b), and (c) that two shots will be awarded.

a.

To determine

Compute the probability that he will make both shots.

Explanation of Solution

Calculation:

The given information is that the Jamal Crawford make 93% of his shots. Assume that late in the basketball game and is awarded two foul shots.

Multiplication Law for Independent Events

For independent events A and B,P(AB)=P(A)×P(B)

The events of making shots are independent events .Required probability is given by:

P(make both shots)=P(make the shot)×P

b.

To determine

Compute the probability that he will make at least one shot.

c.

To determine

Compute the probability that he will miss both shots.

d.

To determine

Compute the probabilities in part (a), (b), and (c). Show that internationally fouling the Portland Trail Blazer’s center is a better strategy than internationally fouling Jamal Crawford.

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