Question

Use the following results from a test for marijuana use, which is provided by a certain drug testing company. Among 147 subjects with positive test results, there are 30 false positive results; among 157 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.)

a. 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.)
b. How many subjects were included in the study?
The total number of subjects in the study was___.
c. How many subjects did not use marijuana?
A total of ___subjects did not use marijuana.

Answer 1

(a)0.615

(b)304

(c)183

Explanation:

Among 147 subjects with positive test results, there are 30 false positive (actually negative) results;

Among 157 negative results, there are 4 false-negative (actual positive) results.

The table below summarises the given data.

`\left\begin{array}cc&$Use Marijuana&$Did Not Use Marijuana&$Total\\---&-------&-------&-------\\$Positive Result&117&30&147\\$Negative Result&4&153&157\\---&-------&-------&-------\\$Total&121&183&304\end{array}\right`

(a)The probability that a randomly selected subject tested negative or did not use marijuana

P(negative or did not use marijuana)

=P(negative)+P(did not use marijuana)-P(both)

`=(157)/(304)+ (183)/(304)-(153)/(304)\\=(187)/(304)\\\\\approx 0.615`

(b)There were a total of 304 subjects in the study.

(c)A total of 183 subjects did not use marijuana.