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 1 1% 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 7%. 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. (Round to four decimal places as needed.)

Answer 1

Solution:-

P(Drugs) = 0.11

P(NonDrug) = 0.89

Positive P( ) = 0.08 Notdru

$P(\frac{Negative}{Drug}) = 0.07$, $P(\frac{Positive}{Drug}) = 0.93$

$P(\frac{Non drug}{Positive}) = \frac{P(NonDrug)\times P(\frac{Positive}{Non-drug})}{P(NonDrug)\times p(\frac{Positive}{Non-drug})+P(Drug)\times P(\frac{Positive}{Drug})}$

$P(\frac{Non drug}{Positive}) = \frac{0.89\times 0.08}{0.89\times 0.08+0.11\times 0.93}$

$P(\frac{Non drug}{Positive}) = 0.4104$