Suppose a drug test is 93% sensitive and 87% specific. That is, the test will produce 93% true positive results for drug users and 87% true negative results for non-drug users. Suppose that 1.8% of people are users of the drug. If a randomly selected individual tests positive, what is the probability he or she is a user

The probability is  

Step-by-step explanation:

Generally a true positive means that the person tested is a drug user and he/she test positive to the test

while true negative mean that the person tested is not a drug user and he/she test negative to the test

From the question we are told that

The probability that a person test positive  to the drug test given that the person is  a drug user is    

Here  P => event that a person test positive to the drug test

         U => event that the person is a drug user

The probability that a person test negative to the drug test given that the person is not a drug user is      

Here  N => event that a person test negative to the drug test

         S => event that the person is not a drug user

The probability that a person is a drug user is  

Generally the probability that a person test positive to the test given that the person is a non- user is  

=>  

Generally the probability that a person is  a non user of drug is  

=>  

Generally the probability that a person test positive to the drug test is mathematically evaluated as

=>  

=>  

Generally the probability a person is a user given that he or she tested positive is mathematically represented as

=>  

=>  

Converting to percentage

=>

b

step-by-step explanation: