b) If the test identifies the employee as a drug user how likely is that the emp
ID: 3253634 • Letter: B
Question
b) If the test identifies the employee as a drug user how likely is that the employee actually is a drug user.
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
a) P(the test will indicate that the employee is a drug user) = P(using drug and positive test) + P(not using drug and positive test)
= 0.2x0.92 + 0.8x0.05
= 0.224
b)P(employee actually is a drug user | test identifies the employee as a drug user) = P(employee actually is a drug user and test identifies the employee as a drug user)/P(test identifies the employee as a drug user)
= 0.2x0.92/0.224
= 0.8214
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