Question

3, A new version of a drug test can detect the drug in subjects us ing the drug 85% of the time. However, it also detects the drug in 10% of people who do not use the drug. If the percentage of drug users in the population is .1%, provide a probabilistic argument against a company policy that will immediately fire anyone who tests positive. Can you suggest a better policy? Justify your answer.

Answer 1

Ans:

P(use drug)=0.001

P(not use drug)=1-0.001=0.999

P(positive/use drug)=0.85

P(positive/not use drug)=0.10

P(positive)=P(positive/use drug)*P(use drug)+P(positive/not use drug)*P(not use drug)

=0.85*0.001+0.10*0.999

=0.10075

P(use drug/positive)=P(positive/use drug)*P(use drug)/P(positive)

=0.85*0.001/0.10075

=0.0084 or 0.84%

The probability that someone is drug user given that test is positive is very very low,which means that test is not effective.If someone test positive,there is very low probability that he or she will be actually drug user.