To reduce theft, the Meredeth Company screens all its employees with a lie detector test that is known to be correct 90 percent of the time (for both guilty and innocent subjects). George Meredeth decides to fire all employees who fail the test. Suppose 5 percent of the employees are guilty of theft.

Question

To reduce theft, the Meredeth Company screens all its employees with a lie detector test that is known to be correct 90 percent of the time (for both guilty and innocent subjects). George Meredeth decides to fire all employees who fail the test. Suppose 5 percent of the employees are guilty of theft.
a. What proportion of the workers are fired?
b. Of the workers fired, what proportion are actually guilty?
c. Of the workers not fired, what proportion are guilty?
d. What do you think of George’s policy?