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# Components arriving at a distributor are checked for ISBN: 9780321629111 32

## Solution for problem 83E Chapter 2

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 83E

Components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors). The first inspector detects 90% of all defectives that are present, and the second inspector does likewise. At least one inspector does not detect a defect on 20% of all defective components. What is the probability that the following occur? a. ?A defective component will be detected only by the first inspector? By exactly one of the two inspectors? b. ?All three defective components in a batch escape detection by both inspectors (assuming inspections of different components are independent of one another)?

Step-by-Step Solution:

Answer Step 1 of 3 P(both detect the defect)=1-P(at least one doesn’t detect) =1-0.2=0.8 Step 2 of 3 a)P(1st detect 2nd doesn’t detect)=P(1st detect)-P(1st detect 2nd detect) =0.9-0.8=0.1 Similarly P(1st doesn’t detect 2nd detect)=0.1 P(exactly one does)=0.1+0.1=0.2

Step 3 of 3

##### ISBN: 9780321629111

This textbook survival guide was created for the textbook: Probability and Statistics for Engineers and the Scientists, edition: 9. Since the solution to 83E from 2 chapter was answered, more than 346 students have viewed the full step-by-step answer. This full solution covers the following key subjects: components, inspectors, inspector, defective, both. This expansive textbook survival guide covers 18 chapters, and 1582 solutions. The answer to “Components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors). The first inspector detects 90% of all defectives that are present, and the second inspector does likewise. At least one inspector does not detect a defect on 20% of all defective components. What is the probability that the following occur? a. ?A defective component will be detected only by the first inspector? By exactly one of the two inspectors? b. ?All three defective components in a batch escape detection by both inspectors (assuming inspections of different components are independent of one another)?” is broken down into a number of easy to follow steps, and 102 words. The full step-by-step solution to problem: 83E from chapter: 2 was answered by , our top Statistics solution expert on 05/06/17, 06:21PM. Probability and Statistics for Engineers and the Scientists was written by and is associated to the ISBN: 9780321629111.

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