Problem

Results from a marijuana drug test study showed 143 subjects with positive test results including 24 false positive results. There were 157 negative results, including 3 false negative results. What is the probability that a randomly selected subject did not use marijuana? Round to three decimal places as needed.
A. 0.533
B. 0.477
C. 0.593
D. 0.523

Answer

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Answer

Final Answer: \(\boxed{0.593}\)

Steps

Step 1 :Let's denote the total number of subjects as \(total\_subjects\), the number of true negatives as \(true\_negatives\), the number of false positives as \(false\_positives\), and the number of non-users as \(non\_users\).

Step 2 :From the problem, we know that \(total\_subjects = 143 + 157 = 300\), \(true\_negatives = 157 - 3 = 154\), and \(false\_positives = 24\).

Step 3 :Then, we can calculate the number of non-users as \(non\_users = true\_negatives + false\_positives = 154 + 24 = 178\).

Step 4 :Finally, we can calculate the probability that a randomly selected subject did not use marijuana as \(probability\_non\_user = \frac{non\_users}{total\_subjects} = \frac{178}{300} = 0.593\).

Step 5 :Final Answer: \(\boxed{0.593}\)

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