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Refer to Exercise 28. Assume that both inspectors inspect

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 29E Chapter 2.3

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 29E

Refer to Exercise 28. Assume that both inspectors inspect every item and that if an item has no flaw, then neither inspector will detect a flaw.

a. Assume that the probability that an item has a flaw is 0.10. If an item is passed by the first inspector, what is the probability that it actually has a flaw?

b. Assume that the probability that an item has a flaw is 0.10. If an item is passed by both inspectors, what is the probability that it actually has a flaw?

Step-by-Step Solution:

Answer:

Step 1 of 3:

                  From the given data we have, the two inspectors inspect every item and that if an item has no flaw, then neither inspector will detect a flaw.

       Let F denoted the event that an item has a flaw. Let A denote the event that a flaw is detected by the first inspector. Let B denote the event that a flaw is detected by the second inspector.

     In exercise 28. We have the probabilities are,

                 

                 

Step 2 of 3:     

a). We have to find the probability that the flaw is found by a first inspector.  

     Given that, the probability that an item has a flaw is 0.10. We are given the probabilities,

       ,

        ,  1 - 0.7

                        = 1- 0.9                             = 0.3

                        = 0.1

     

                   = 1- 0.1

                   = 0.9  

     

      Using by Bayes rule

        

                          =

                          =

   

           = 0.01

        Therefore, the probability that the flaw is found by a first inspector is 0.01.

   

Step 3 of 3

Chapter 2.3, Problem 29E is Solved
Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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Refer to Exercise 28. Assume that both inspectors inspect

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