¬ virus infects one in every 400 pea Et the virus in a person is positive 9 on has the virus and positive 5% of loes not have the virus. (This 5% re sitive.) Let A be the event "the per- e the event "the person tests positiv
¬ virus infects one in every 400 pea Et the virus in a person is positive 9 on has the virus and positive 5% of loes not have the virus. (This 5% re sitive.) Let A be the event "the per- e the event "the person tests positiv
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Understanding Conditional Probabilities in Viral Testing**
A certain virus infects **one in every 400 people**. A test used to detect the virus in a person is positive **90%** of the time if the person has the virus and positive **5%** of the time if the person does not have the virus. (This 5% result is called a false positive.) Let A be the event "the person is infected" and B be the event "the person tests positive".
The following table displays the test results for a population of 100,000 people:
| | Positive | Negative | Totals |
|----------|----------|----------|---------|
| **Virus** | 225 | 25 | 250 |
| **No virus**| 4987.5 | 94762.5 | 99750 |
| **Totals** | 5212.5 | 94787.5 | 100000 |
### Questions:
a. **Find the probability that a person has the virus given that they have tested positive**, i.e., find \( P(A | B) \). Round your answer to the nearest hundredth of a percent and do not include a percent sign.
\[ P(A \text{ if } B) = \frac{\text{Number of true positives}}{\text{Total number of positives}} = \frac{225}{5212.5} \approx 4.32\% \]
b. **Find the probability that a person does not have the virus given that they test negative**, i.e., find \( P(\text{not } A | \text{not } B) \). Round your answer to the nearest hundredth of a percent and do not include a percent sign.
\[ P(\text{not } A \text{ if not } B) = \frac{\text{Number of true negatives}}{\text{Total number of negatives}} = \frac{94762.5}{94787.5} \approx 99.97\% \]
### Explanation of the Table:
The table is divided into two main categories: individuals who have the virus and individuals who do not have the virus. For each category, there are data points on the number of positive and negative test results.
- **Virus (225 Positive, 25 Negative, 250 Total)**
- This row indicates that among the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95e5613b-1a25-4b20-8027-b25d1244d9dc%2F47434cb9-aada-463c-b5f1-4fa6a51505e8%2Fzmpvs49_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Conditional Probabilities in Viral Testing**
A certain virus infects **one in every 400 people**. A test used to detect the virus in a person is positive **90%** of the time if the person has the virus and positive **5%** of the time if the person does not have the virus. (This 5% result is called a false positive.) Let A be the event "the person is infected" and B be the event "the person tests positive".
The following table displays the test results for a population of 100,000 people:
| | Positive | Negative | Totals |
|----------|----------|----------|---------|
| **Virus** | 225 | 25 | 250 |
| **No virus**| 4987.5 | 94762.5 | 99750 |
| **Totals** | 5212.5 | 94787.5 | 100000 |
### Questions:
a. **Find the probability that a person has the virus given that they have tested positive**, i.e., find \( P(A | B) \). Round your answer to the nearest hundredth of a percent and do not include a percent sign.
\[ P(A \text{ if } B) = \frac{\text{Number of true positives}}{\text{Total number of positives}} = \frac{225}{5212.5} \approx 4.32\% \]
b. **Find the probability that a person does not have the virus given that they test negative**, i.e., find \( P(\text{not } A | \text{not } B) \). Round your answer to the nearest hundredth of a percent and do not include a percent sign.
\[ P(\text{not } A \text{ if not } B) = \frac{\text{Number of true negatives}}{\text{Total number of negatives}} = \frac{94762.5}{94787.5} \approx 99.97\% \]
### Explanation of the Table:
The table is divided into two main categories: individuals who have the virus and individuals who do not have the virus. For each category, there are data points on the number of positive and negative test results.
- **Virus (225 Positive, 25 Negative, 250 Total)**
- This row indicates that among the
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