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A chemical engineer is interested in determining whether a

Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye ISBN: 9780321629111 32

Solution for problem 97E Chapter 2

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

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Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye

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

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Problem 97E

A chemical engineer is interested in determining whether a certain trace impurity is present in a product. An experiment has a probability of .80 of detecting the impurity if it is present. The probability of not detecting the impurity if it is absent is .90. The prior probabilities of the impurity being present and being absent are .40 and .60, respectively. Three separate experiments result in only two detections. What is the posterior probability that the impurity is present?

Step-by-Step Solution:

Answer: Step 1 of 1 Given, P(Detect | Present) = 0.8 P(Detect | Absent) = 0.1 P(Not detect | Present) = 0.2 P(Not detect | Absent) = 0.9 P(Present) = 0.4 P(Absent) = 0.6 Three separate experiments result in only two detections. The posterior probability that the impurity is present is given by P(Present | 2 detection out of 3) = P(2 detection Present) P(2 detection) P(AB) From the conditional...

Step 2 of 3

Chapter 2, Problem 97E is Solved
Step 3 of 3

Textbook: Probability and Statistics for Engineers and the Scientists
Edition: 9
Author: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye
ISBN: 9780321629111

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