Question

In Exercises 21–24, use these results from the “1-Panel-THC” test for marijuana use, which is provided by the company Drug Test Success: Among 143 subjects with positive test results, there are 24 false positive results; among 157 negative results, there are 3 false negative results. (Hint: Construct a table similar to Table 4-1, which is included with the Chapter Problem.)

Testing for Marijuana Use

a. How many subjects are included in the study?

b. How many of the subjects had a true negative result?

c. What is the probability that a randomly selected subject had a true negative result?

Short answer

a.The number of subjects is equal to 300.

b.The number of subjects who had a true negative result is equal to 154.

c.The probability of selecting a subject who had a true negative result is equal to 0.513.

Step-by-step solution

Given information

The given data shows the number of positive and negative drug test results of subjects.

The values are categorized as true and false results.

Define probability

For an event A, the probability of its occurrence is computed as shown below:

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

Calculation

The table below shows the number of subjects that fall in each category:

	True Result	False Result	Total
Subject Tested Positive	143 – 24 =119	24	143
Subject Tested Negative	157 – 3 = 154	3	157
Total	273	27	Grand Total=300

a.

The total number of subjects is given as follows:

$119+24+154+3=300$

Therefore, the total number of subjects is equal to300.

b.

The number of subjects who had a true negative test result is given by:

$157-3=154$

Therefore, the number of subjects who had a true negative test result is equalto 154.

c.

Theprobability of selecting a subject who had a true negative test result is given as follows:

$$\begin{gathered} P\left(\text{True}\text{negative}\text{result}\right)=\frac{\text{Number}\text{of}\text{subjects}\text{who}\text{had}\text{a}\text{true}\text{negative}\text{result}}{\text{Total}\text{number}\text{of}\text{subjects}} \\ =\frac{154}{300} \\ =0.513 \end{gathered}$$

Therefore, the probability of selecting a subject who had a true negative test result is equalto 0.513.