I personally have used statistics in trying to challenge the reliability of drug testing results. Suppose the chance of a mistake in the taking and processing of a urine sample for a drug test is just 1 in 100. And your client has a "dirty" (i.e., positive) test result. Only a 1 in 100 chance that it could be wrong? Not necessarily. If the vast majority of all tests given- say 99 in 100-are truly clean, then you get one false dirty and one true dirty in every 100 tests, so that half of the dirty tests are false. TD = event that the test result is dirty %3D TC = event that the test result is clean D = event that the person tested is actually dirty %3D C = event that the person tested is actually clean P(TD|D) = 0.99 P(C) = 0.99 P(TD|C) = 0.01 P(D)=0.01 (a) What is the probability of a random test resulting in dirty? (b) What is the probability of person being clean given that their test re- sult is dirty? Is this consistent with the quote given?

I personally have used statistics in trying to challenge the reliability of drug testing results. Suppose the chance of a mistake in the taking and processing of a urine sample for a drug test is just 1 in 100. And your client has a "dirty" (i.e., positive) test result. Only a 1 in 100 chance that it could be wrong? Not necessarily. If the vast majority of all tests given- say 99 in 100-are truly clean, then you get one false dirty and one true dirty in every 100 tests, so that half of the dirty tests are false. TD = event that the test result is dirty %3D TC = event that the test result is clean D = event that the person tested is actually dirty %3D C = event that the person tested is actually clean P(TD|D) = 0.99 P(C) = 0.99 P(TD|C) = 0.01 P(D)=0.01 (a) What is the probability of a random test resulting in dirty? (b) What is the probability of person being clean given that their test re- sult is dirty? Is this consistent with the quote given?

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter8: Sequences, Series,and Probability

Section8.7: Probability

Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....

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