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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.

- 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.

**a.**

To determine

Compute the probability that he will make both shots.

**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,*

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

**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.

STATISTICS F/BUSINESS+ECONOMICS-TEXT

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