Question

use the following results from a test for marijuana use, which is provided by a certain drug testing company. among 142 subjects with positive test results, there are 20 false - positive results. among 154 negative results, there are 2 false negative results. complete parts (a) through (c). (hint: construct a table.)
a. how many subjects were included in the study?
the total number of subjects in the study was 296.
b. how many subjects did not use marijuana?
a total of 172 subjects did not use marijuana.
c. what is the probability that a randomly selected subject did not use marijuana?
the probability that a randomly selected subject did not use marijuana is .
(do not round until the final answer. then round to three decimal places as needed.)

Explanation:

Step1: Recall probability formula

The probability $P(A)$ of an event $A$ is given by $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$.

Step2: Identify favorable and total outcomes

The number of subjects who did not use marijuana is 172 (from part b), and the total number of subjects in the study is 296 (from part a).
So, the probability $P$ that a randomly - selected subject did not use marijuana is $P=\frac{172}{296}$.

Step3: Calculate and round

$P=\frac{172}{296}\approx0.581$

Answer:

$0.581$