of the
Week
|
Problem
of the Week |
This week's problem is being handled by Professor Ollie Nanyes.
A company wants to test employees for drug use. They have 5000 employees. The company settles on a drug test that is 99% accurate in that if the person who was tested actually used drugs, the test would be positive 99% of the time, and if the person who was tested actually did not use drugs, the test would be negative 99% of the time.
Research has shown that, on the average, 5% of the population uses the drugs that the company is testing for.
Given that an employee has received a "positive" drug test (i. e., the test indicated that this employee used drugs), what is the probability that this employee really is a drug user?
What accuracy does the company need its drug test achieve in order to be certain that, 99% of the time, someone who tests "positive" reading on their drug test really is a drug user?
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