Question

Use the following results from a test for marijuana use, which is provided by a certain drug testing company. Among 148 subjects with positive test results, there are 28 false positive results. Among 150 negative results, there are 5 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 _______ 

b. How many subjects did not use marijuana?

A total of _______  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 _______ 

Answer 1

First let's see what are false positive and false negative results.

In medical testing, and more generally in binary classification, a false positive is an error in data reporting in which a test result improperly indicates presence of a condition, such as a disease (the result is positive), when in reality it is not present, while a false negative is an error in which a test result improperly indicates no presence of a condition (the result is negative), when in reality it is present.

Given that among 148 subjects with positive test result for marijuana consumption, 28 were false positive results and among 150 subjects with negative test results, 5 were false negatives.

Therefore, out of 148 subjects who were tested positive, 28 were actually negative so out of 148 subjects only 148-28 = 120 actually used marijuana and 28 did not.

And, out of 150 subjects who were tested negative, 5 were actually positive so only 150-5=145 actually did not use marijuana and 5 did.

a) The total number of subjects in the study was 148+150 = 298

b) A total of 28+145 = 173 subjects did not use marjuana.

c) The probability that a randomly selected subject did not use marijuana is =(number of subjects who did not use marijuana / Total number of subjects) = 173/298 = 0.581

Hope it helps! Please give a thumbs up if it does and feel free to ask any question in the comments.