Question

5. A company is having random drug tests in the workplace. The lab-test the company is using produces false negatives 2% of the time and false positives 5% of the time. Assume that 10% of the employees at this company use drugs. a. If an employee tests positive for drug use, what is the probability that he/she does not use drugs? Show your work. [2 points] b. What is the probability a drug user tests negative twice in a row? Show/explain your work. [2 points] c. A non-drug user was tested positive for drug use. In response to her/his complaint, the company agreed to conduct her/his drug test again. What is the probability that her/his test will turn positive again? Show/explain how you arrived at your work. [2 points]

Answer 1

a)

P(tested positive)=P(use drugs and tested positive)+P(not use drugs and tested positive)=0.1*(1-0.02)+(1-0.1)*0.05=0.143

therefore P(not use drugs given tested positive)=P(not use drugs and tested positive)/P(tested positive)=(1-0.1)*0.05/0.143

=0.314685

b) probability a drug user tests negative twice in a row =0.02*0.02 =0.0004

c)

probability that her/his test will turn positive again =P(tested positive given not uses)=0.05 (as it is independent of prior test)