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It is known that two defective copies of a commercial

Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger ISBN: 9781118539712 55

Solution for problem 213SE Chapter 2.8

Applied Statistics and Probability for Engineers | 6th Edition

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Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger

Applied Statistics and Probability for Engineers | 6th Edition

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Problem 213SE

Problem 213SE

It is known that two defective copies of a commercial software program were erroneously sent to a shipping lot that now has a total of 75 copies of the program. A sample of copies will be selected from the lot without replacement.

(a) If three copies of the software are inspected, determine the probability that exactly one of the defective copies will be found.

(b) If three copies of the software are inspected, determine the probability that both defective copies will be found.

(c) If 73 copies are inspected, determine the probability that both copies will be found. (Hint: Work with the copies that remain in the lot.)

Step-by-Step Solution:

Answer

Step 1 of 3

(a)

It is known that two defective copies of a commercial software program were erroneously sent to a shipping lot that now has a total of  copies of the program.

A sample of copies will be selected from the lot without replacement.

we are asked to find the probability that exactly one of the defective copies will be found if three copies of the software are inspected.

Let  denote the defective copy of the software.

Let  denote the original copy of software or without defect

The number of ways we can inspect exactly one defects from the three copies of the software is using combination theorem since the sample of copies are selected from the lot without replacement.

We can write our sample space of exactly one defects,

……..(1)

The probability of defective copies from the shipping lot that has a total of  copies is,

The probability that exactly one of the defective copies is using equation (1)

Hence the probability that exactly one of the defective copies will be found is  


Step 2 of 3

Chapter 2.8, Problem 213SE is Solved
Step 3 of 3

Textbook: Applied Statistics and Probability for Engineers
Edition: 6
Author: Douglas C. Montgomery, George C. Runger
ISBN: 9781118539712

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It is known that two defective copies of a commercial