Given the results from a marijuana test conducted by a …

Mathematics Questions

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

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-by-Step Solution

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 ‚Äöa¬© 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.

Related Concepts

Test Results

The outcomes of assessing the performance of a test by examining positive and negative results alongside false classifications.

True Positives

The number of subjects correctly identified as having the condition being tested for, calculated by subtracting false positives from total positives.

Probability

A mathematical representation of the likelihood of an event occurring, often expressed as a fraction or decimal between 0 and 1.

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