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 got a result that is a false positive. Who would suffer from a false positive result? Why?

Short answer

The probability of selecting a person who got a false positive result is 0.0450.

The candidate will suffer from a false positive result because of the risk of losing the job despite not using drugs.

Step-by-step solution

Given information

In a sample, 555 subjects are tested for drug use and classified into four different categories.

One subject is selected at random.

Define probability

Probability is a measure that quantifies the likelihood of the occurrence of an event.

Mathematically, it can be written as

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

Calculate the probability 

Let E be the event that a randomly selected person got a false positive result.

The total number of persons who got tested is 555.

The number of persons who got a false positive test result is 25.

The probability of eventA is

$$\begin{gathered} P\left(A\right)=\frac{Numberofpersonswhotestedfalsepositive}{Totalnumberofpersons} \\ =\frac{25}{555} \\ =0.04504 \end{gathered}$$

Therefore, the probability of selecting a person who got a false positive test result is 0.0450.

Discuss the impact of the result

A false positive result implies that the person is tested positive for using drugs when they do not use them.

The randomly selected person who tests false positive will suffer as they would risk losing the job.