In Exercises 21–24, refer to the sample data in Table 4-1, which is included with the Chapter Problem. Assume that 1 of the 555 subjects included in Table 4-1 is randomly selected.

	Positive Test Result (Test shows drug use)	Negative Test Result (Test shows no drug use)
Subject Uses Drugs	45 (True Positive)	5 (False Negative)
Subject Does Not Use drugs	25 (False Positive)	480 (True Negative)

Drug Testing Job Applicants Find the probability of selecting someone who got a result that is a false negative. Who would suffer from a false negative result? Why?

Data are given in 4 categories depending on the true condition versus the test results for a sample of 555 people.

Probability is the number of outcomes that result in an event (E) divided by the total number of outcomes.

It is computed using the formula

$P\left(E\right)=\frac{\text{Number}\text{of}\text{favourable}\text{outcomes}\text{of E}}{\text{Total}\text{number}\text{of}\text{outcomes}}$

Let A be the event of selecting a person who got a false negative result.

The total number of persons who were tested is 555.

The number of persons who got a false negative test result is 5.

The probability of event A is

$$\begin{gathered} P\left(A\right)=\frac{Numberofpersonswhotestedfalsenegative}{Totalnumberofpersons} \\ =\frac{5}{555} \\ =0.00901 \end{gathered}$$

Therefore, the probability of selecting a person who got a false negative test result is 0.00901.

It can be concluded that the employer will suffer from a false negative test result.

The randomly selected person would test negative for the use of drugs when he actually uses them.

For such a subject, the employer would be at the risk of hiring a person who continues to use drugs.