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?
a. 0.95 of the workers are innocent, and of those, 0.1 will be detected as guilty. This is 0.095 of the workers in total.
0.05 of the workers are guilty, and of those, 0.9 will be detected. This is 0.045 of the workers in total. Therefore, 0.095 + 0.045 = 0.14 of the workers are fired.
b. From a, we can see that the ratio of innocent to guilty is 0.095:0.045.
So, the proportion of guilty people is 0.045/0.14 ≈ 0.32
c. 0.05 of the workers were guilty, and 0.1 of those were not fired, so the total non-fired guilty people is 0.005.
0.86 of the workers were not fired, so the proportion of those that are guilty is 0.005/0.86 ≈ 0.0058
d. This question is based on opinion, so you need to answer this one yourself.
Why did the vector cross the road?
It wanted to be normal.