Question

use the following results from a test for marijuana use, which is provided by a certain drug testing company. among 150 subjects with positive test results, there are 20 false - positive results; among 151 negative results, there are 4 false - negative results. if one of the test subjects is randomly selected, find the probability that the subject tested negative or did not use marijuana. (hint: construct a table.) the probability that a randomly selected subject tested negative or did not use marijuana is . (do not round until the final answer. then round to three decimal places as needed.)

Explanation:

Step1: Construct the contingency - table

Positive test results: 150, False - positive: 20, so True - positive = 150 - 20 = 130.
Negative test results: 151, False - negative: 4, so True - negative = 151 - 4 = 147.
The total number of subjects = 150+151 = 301.
The number of subjects who did not use marijuana = False - positive+True - negative = 20 + 147=167.
The number of subjects who tested negative = 151.
The number of subjects who tested negative and did not use marijuana = True - negative = 147.

Step2: Use the addition rule of probability

The addition rule for two events A and B is \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\).
Let A be the event that the subject tested negative and B be the event that the subject did not use marijuana.
\(P(A)=\frac{151}{301}\), \(P(B)=\frac{167}{301}\), \(P(A\cap B)=\frac{147}{301}\).
\(P(A\cup B)=\frac{151 + 167-147}{301}=\frac{171}{301}\approx0.568\)

Answer:

0.568