Chapter 11.4, Problem 78E

The president of a large company with 10,000 employees is considering mandatory cocaine testing for every employee. The test that would be used is 90% accurate, meaning that it will detect 90% of the cocaine users who are tested, and that 90% of the nonusers will test negative. This also means that the test gives 10% false positive. Suppose that 1% of the employees actually use cocaine. Find the probability that someone who tests positive for cocaine use is, indeed, a user.

Hint: Find the following probability fraction:

$\frac{\text{the number of employees who test positive and are cocaine users}}{\text{the number of employees who test positive This fraction is given by}}.$

$\frac{\text{90\% of 1\% of 10,000}}{\begin{array}{l}\text{the number who test positive who actually use }\\ \text{cocaine plus the number who test positive }\\ \text{who do not use cocaine}\end{array}}$

What does this probability indicate in terms of the percentage of employees who test positive who are not actually users? Discuss these numbers in terms of the issue of mandatory drug testing. Write a paper either in favor of or against mandatory drug testing, incorporating the actual percentage accuracy for such tests.