Questions: 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 27 false positive results; among 160 negative results, there are 2 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.) 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.)

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 27 false positive results; among 160 negative results, there are 2 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.)

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.)

Transcript text: 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 27 false positive results; among 160 negative results, there are 2 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.) The probability that a randomly selected subject tested negative or did not use marijuana is $\square$ (Do not round until the final answer. Then round to three decimal places as needed.)

Solution

Solution Steps

Step 1: Construct a Contingency Table

Given the total number of subjects $N$ = 307, positive test results $P$ = 147, false positive results $FP$ = 27, and false negative results $FN$ = 2. We calculate True Positive $TP$ = $P - FP$ = 120 and True Negative $TN$ = $N - P - FN$ = 158.

Step 2: Calculate Probabilities

The probability of a false positive or false negative is calculated as $ rac{FP + FN}{N}$ = 0.094. The probability that a subject tested negative or did not use the substance is calculated as $ rac{TN + (N - P - TN)}{N}$ = 0.521.