Use the following results from a test for marijuana use, which is provided by a certain drug testing company. Among 146 subjects with positive test results, there are 30 false positive results; among 159 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.)

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**Understanding Probability in Drug Testing**

In a study conducted by a drug testing company, data from a marijuana test result is recorded as follows:

- There are 146 subjects who tested positive.
- Out of these, 30 results were false positives.
- There are 159 subjects who tested negative.
- Among these negative results, 2 were false negatives.

**Objective:**

Calculate the probability that a randomly selected subject either tested negative or did not use marijuana.

**Steps to Solve:**

1. **Construct a Table**: First, organize the data to distinguish between true and false test results, both positive and negative.
   
2. **Calculate Total Subjects**: 
   - True Positives = 146 - 30 = 116
   - True Negatives = 159 - 2 = 157
   - Total Subjects: True Positives + True Negatives + False Positives + False Negatives

3. **Determine Desired Outcomes**:
   - The probability of a subject testing negative or did not use marijuana includes true negatives and false positives.

4. **Compute Probability**:
   - Find the ratio of the desired outcomes to the total number of subjects.
   - Use the formula: Probability = (True Negatives + False Positives) / Total Subjects.
   - Ensure the final probability is rounded to three decimal places.

In this setup, you have everything needed to complete the calculation and understand the testing accuracy and real-world implications of such drug test results.
Transcribed Image Text:**Understanding Probability in Drug Testing** In a study conducted by a drug testing company, data from a marijuana test result is recorded as follows: - There are 146 subjects who tested positive. - Out of these, 30 results were false positives. - There are 159 subjects who tested negative. - Among these negative results, 2 were false negatives. **Objective:** Calculate the probability that a randomly selected subject either tested negative or did not use marijuana. **Steps to Solve:** 1. **Construct a Table**: First, organize the data to distinguish between true and false test results, both positive and negative. 2. **Calculate Total Subjects**: - True Positives = 146 - 30 = 116 - True Negatives = 159 - 2 = 157 - Total Subjects: True Positives + True Negatives + False Positives + False Negatives 3. **Determine Desired Outcomes**: - The probability of a subject testing negative or did not use marijuana includes true negatives and false positives. 4. **Compute Probability**: - Find the ratio of the desired outcomes to the total number of subjects. - Use the formula: Probability = (True Negatives + False Positives) / Total Subjects. - Ensure the final probability is rounded to three decimal places. In this setup, you have everything needed to complete the calculation and understand the testing accuracy and real-world implications of such drug test results.
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