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 156 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: Con
Accepted Solution
A:
Answer:The required probability is 0.6053Step-by-step explanation:Consider the provided information.Among 148 subjects with positive test results, there are 28 false positive results.That means the true positive results are: 148-28=120Among 156 negative results, there are 4 false negative results.That means the positive results are 156-4=152 Positive Negative Total
Use marijuana F negative 120 4 124
Not use marijuana F positive 28 152 180 Total 148 156 304 The probability that the subject tested negative or did not use marijuana.P(Negative∪ not use marijuana)=[P(Negative)+P(Not use marijuana)-P(negative ∩ not use marijuana)]P(Negative∪ not use marijuana) = [tex]\frac{156}{304} +\frac{180}{304} -\frac{152}{304}[/tex]P(Negative∪ not use marijuana) = [tex]\frac{156+180-152}{304}[/tex]P(Negative∪ not use marijuana) = [tex]\frac{184}{304}[/tex]P(Negative∪ not use marijuana) ≈ [tex]0.6053[/tex]Hence, the required probability is 0.6053