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Each of three football players will attempt to kick a

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman ISBN: 9780321923271 41

Solution for problem 7E Chapter 1.4

Probability and Statistical Inference | 9th Edition

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Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Probability and Statistical Inference | 9th Edition

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Problem 7E

PROBLEM 7E

Each of three football players will attempt to kick a field goal from the 25-yard line. Let Aidenote the event that the field goal is made by player i, i = 1, 2, 3. Assume that A1, A2, A3 are mutually independent and that P(A1) = 0.5, P(A2) = 0.7, P(A3) = 0.6.

(a) Compute the probability that exactly one player is successful.

(b) Compute the probability that exactly two players make a field goal (i.e., one misses).

Step-by-Step Solution:

Answer :

Step 1 of 3 :

Given, each of three football players will attempt to kick a field goal from the 25-yard line.

Let denote the event that the field goal is made by player i , where i = 1, 2, 3.

We have to assume that ,  and are mutually independent

Where, P() = 0.5 , P() = 0.7 and P() = 0.6

Step 2 of 3 :

     

         The claim is to find the probability that exactly one player is successful

    P(exactly one player successful) = P(+ P(  +  

                                                           P(        

Where ,  = 1 -

                    = 1  - 0.5

                   = 0.5

 = 1 -

               = 1  - 0.7  

                = 0.3

and

 = 1 -

                    = 1  - 0.6

                   = 0.4

P(exactly one player successful) = (050.3 0.4)  + ( 0.50.7 0.4) +

                                                         ( 0.50.3 0.6)

                                                     = 0.06  + 0.14 + 0.09

                                                      = 0.29

Therefore, the probability that exactly one player is successful is 0.29

Step 3 of 3

Chapter 1.4, Problem 7E is Solved
Textbook: Probability and Statistical Inference
Edition: 9
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
ISBN: 9780321923271

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