Question

A supreme court from a certain region recently ruled that employees can be tested for drugs only if management has reasonable cause to administer the test. An article in a certain magazine focused on the misclassification rates of such drug tests. A false positive occurs when a drug test administered to a​ non-drug user yields a positive result. A false negative occurs when a drug test administered to a drug user yields a negative result. Complete parts a and b. a. The author presented the following​ scenario: Suppose that 6​% of a population of workers consists of drug users. The drug test has a false positive rate​ (the probability of a positive drug test given the worker is a​ non-drug user) of 8​% and a false negative rate​ (the probability of a negative drug test given the worker is a drug​ user) of 3​%. A worker selected from this population is drug tested and found to have a positive result. What is the probability that the worker is a​ non-drug user?

Apply​ Bayes' Rule to obtain your answer. 0.5637

​(Round to four decimal places as​ needed.)

b. Recall that in the​ region, drug tests can be administered only with probable cause.​ Hence, for workers that are​ tested, it is likely that a high proportion of them use drugs. Now consider a population of workers in which 89​% are drug users.​ Again, assume the false positive rate of the drug test is 8​% and the false negative rate of the drug test is 3​%. A worker selected from this population is drug tested and found to have a positive result. What is the probability that the worker is a​ non-drug user? nothing ​(Round to four decimal places as​ needed.)

Answer 1