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 23 false positive results; among 154 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: 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 23 false positive results; among 154 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: 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.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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Question 10
![**Title: Evaluating the Accuracy of Drug Test Results**
**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 23 false positive results; among 154 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: Construct a table.)
---
**Question:**
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.)
---
**Analysis:**
To solve this problem, we can use a table to organize the given information and then calculate the required probability.
First, let’s break down the information:
- Total subjects who tested positive: 147
- False positives among them: 23
- True positives (actual marijuana users) = 147 - 23 = 124
- Total subjects who tested negative: 154
- False negatives among them: 4
- True negatives (actual non-users) = 154 - 4 = 150
So, the total number of subjects:
- Total positive results = 147
- Total negative results = 154
- Total subjects = 147 + 154 = 301
To find the probability that a randomly selected subject tested negative or did not use marijuana, we need to consider:
- True negatives (150)
- False negatives (4)
- Subjects who do not use marijuana = true negatives + false positives = 150 + 23 = 173
Events (subject tested negative or did not use marijuana):
- Total good outcomes (test negative or did not use marijuana) = true negatives + false negatives + false positives = 150 + 23 + 4 = 177
Finally, the probability is calculated as follows:
\[ \text{Probability} = \frac{\text{Total good outcomes}}{\text{Total subjects}} = \frac{177}{301} \]
Let's calculate the value:
\[ \text{Probability} = \frac{177}{301} \approx 0.588 \]
Hence, the probability that a randomly selected subject tested negative or did not use marijuana is approximately 0.588 (rounded to three decimal places).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6a767b23-c124-4e33-a8c8-1cb736a4d72e%2Fcaefcc64-b0d7-4cb7-864e-c2329d53949e%2Fntrlkewp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Evaluating the Accuracy of Drug Test Results**
**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 23 false positive results; among 154 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: Construct a table.)
---
**Question:**
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.)
---
**Analysis:**
To solve this problem, we can use a table to organize the given information and then calculate the required probability.
First, let’s break down the information:
- Total subjects who tested positive: 147
- False positives among them: 23
- True positives (actual marijuana users) = 147 - 23 = 124
- Total subjects who tested negative: 154
- False negatives among them: 4
- True negatives (actual non-users) = 154 - 4 = 150
So, the total number of subjects:
- Total positive results = 147
- Total negative results = 154
- Total subjects = 147 + 154 = 301
To find the probability that a randomly selected subject tested negative or did not use marijuana, we need to consider:
- True negatives (150)
- False negatives (4)
- Subjects who do not use marijuana = true negatives + false positives = 150 + 23 = 173
Events (subject tested negative or did not use marijuana):
- Total good outcomes (test negative or did not use marijuana) = true negatives + false negatives + false positives = 150 + 23 + 4 = 177
Finally, the probability is calculated as follows:
\[ \text{Probability} = \frac{\text{Total good outcomes}}{\text{Total subjects}} = \frac{177}{301} \]
Let's calculate the value:
\[ \text{Probability} = \frac{177}{301} \approx 0.588 \]
Hence, the probability that a randomly selected subject tested negative or did not use marijuana is approximately 0.588 (rounded to three decimal places).
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