Short Answer
The assessment of test results identifies 120 true positives and 152 true negatives from a total of 304 subjects. The calculated probability that a subject tested negative or did not use marijuana is approximately 0.6053.
Step 1: Assess Test Results
Begin by reviewing the total number of subjects involved in the test results. You have:
- 148 subjects tested positive, with 28 false positives.
- This indicates that the true positive outcomes are calculated as 148 – 28 = 120 true positives.
Additionally, among 156 negative results, there are 4 false negatives, leading to 156 – 4 = 152 positive outcomes possible.
Step 2: Compile Total Outcomes
Next, gather all results into a consolidated format. Here’s how they break down:
- True Positives: 120
- False Positives: 28
- True Negatives: 152
- False Negatives: 4
When compiled, the total outcomes total up to 304 subjects which includes both positive and negative test results.
Step 3: Calculate Required Probability
Now compute the probability that a subject tested negative or did not use marijuana using the formula:
- P(Negative) = 156/304
- P(Not use marijuana) = 180/304
- P(Negative ‚a© Not use marijuana) = 152/304
Substituting these into the probability formula, we find:
P(Negative ‚Äöa‚Ñ¢ Not use marijuana) = (156 + 180 – 152) / 304 = 184 / 304 ‚Äöaa 0.6053.
This concludes that the required probability is approximately 0.6053.