b) If the test identifies the employee as a drug user,how likely is that the emp

Question

b) If the test identifies the employee as a drug user,how likely is that the employee is a drug user.

Please use contigency table and solve.Thank you.

You are about to implement a drug-testing procedure for company employees. In a recent anonymous survey, 20% of your employees admitted to using illegal drugs. The random drug testing procedure you are about to employ is not infallible. In fact, about 5% of the time, it will produce a false positive, that is, if the person being tested is NOT a drug user, there is a 5% probability that the test will nevertheless identify that person as a drug user. The test also has a probability of 0.08 of producing a false negative about 8% of the time a drug user will be identified as a non-user. a. (1 pt) If an employee is chosen at random, how likely is it that the test will indicate that the employee is a drug user?

Explanation / Answer

here let probabilty of drug user =P(D) and probabilty of not using drug =P(ND)

also probbailty of positive test P(PT) and that of negative test =P(NT)

a) from above contingency table probabilty of positive test =0.224

b) probabilty of a person being drug user given tested positive =P(D|TP)=0.184/0.224= 0.8214

D ND Total PT 0.2*0.92=0.184 0.80*0.05=0.04 0.184+0.04=0.224 NT 0.2-0.184=0.016 0.8-0.04=0.76 0.016+0.76=0.776 Total 0.2 0.8 1

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