Explanation Given Information: There are 1000 people. In a laboratory, false negative results produced is 2 % and false positive results is 5 % . A company hires that laboratory in which 10 % of the employee uses drugs. Formula Used: Steps to evaluate the probability using natural frequencies: Step 1: Find the starting event and insert it as a root node. Step 2: Find the other events dependent on these event branch. Step 3: Then, on each branch the occurrences of the event is placed. Step 4: Determine the probability which is the product of its probability along with the probability of all previous dependent events. Calculation: Consider the number of people to be 1000 . Start the tree diagram with root node: Then, compute the probability of all branch events which is the product of its probability along with the probability of all previous dependent events as, The number of employees who uses drugs is, B 1 = ( Percentage of employees who uses drugs ) ( total number of employees ) = ( 10 100 ) ( 1000 ) = 100 The number of employees who does not use drugs is, B 2 = ( Total number of employees ) − ( number of employees who uses drugs ) = 1000 − 100 = 900 Then, the tree diagram with branch events: Further, calculate the count of all branch events as, The number of employees who uses drugs and results false negative is, B 3 = ( Percentage of false negative result ) ( number of employees who uses drugs ) = ( 2 100 ) ( 100 ) = 2 The number of employee use drugs who have correct results is, B 4 = (

Finite Mathematics & Its Applications (12th Edition)

12th Edition

ISBN: 9780134437767

Author: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair

Publisher: PEARSON

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Chapter 6.6, Problem 26E

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To calculate: The probability that an employee actually uses drugs if an employee tests positive for drug use. In a drug testing laboratory, there are 1000 people, false negative results produced is 2% and false positive results is 5%. A company hires that laboratory and 10% of the employee uses drugs. Use the method of natural frequencies.

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Chapter 6.6, Problem 25E

Chapter 6.6, Problem 27E

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Chapter 6 Solutions

Finite Mathematics & Its Applications (12th Edition)

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Solution Summary: The author explains how to calculate the probability that an employee actually uses drugs in a drug testing laboratory.

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