Question

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 uses drugs. Does the result appear to be reasonable as an estimate of the “prevalence rate” described in the Chapter Problem?

Short answer

The probability of selecting a person who uses drugs is 0.0901.

No, the value does not appear to be reasonable for estimating the prevalence rate.

Step-by-step solution

Given information

For a job, 555 candidates are drug tested, and their results are tabulated under four categories.

One of these candidates is chosen at random.

Define probability

Probability gives an idea of how plausible an event is.

It is expressed as

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

Calculate the probability

Let A be the event of selecting a person who uses drugs.

Here, the number of people who use drugs is the sum of the two categories:

• The number of people who tested true positive (45)
• The number of people who tested false negative (5)

The total number of persons who got tested is 555.

The probability of event A is

$$\begin{gathered} P\left(A\right)=\frac{Numberofpersonswhousedrugs}{Totalnumberofpersons} \\ =\frac{45+5}{555} \\ =\frac{50}{555} \\ =0.0901 \end{gathered}$$

Therefore, the probability of selecting a person who uses drugs is 0.0901.

Discuss the prevalence rate

The prevalence rate is the number of subjects in the population who are affected by the condition. The actual estimate is the set of subjects who use drugs.

The computed probability does not appear to be a reasonable estimate of the actual prevalence level.