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Question:
Bim en
Ee
led
EB ie oo se csr rent on UO
ERE
=
Cs SUSE
| mg be heh 1 cement in rss se ber amen he ues bo You
E Tre
If =
| ft ten
ee eee IE
Be roar cometh
Hl res
This is AI generated Response.
Asked by: Sunitha
Created at: 2025-10-20 11:06:27
Asked by: Sunitha
Created at: 2025-10-20 11:06:27
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# Explanation the COVID-19 Test Results## Part a) - Probability the person is infected a positive test### Given Data:
| Test Positive | Test Negative | Total |
|----------------|-----------------|-|------------|
| **Infected | .01 .2 . |
|Not Infected | .001 .5 | . |
| **Total Prob** | .011 | .7 | 1. |
### Calculation:
\[ P(\text{Infected} | \text{Test Positive}) = \frac{P(\text{Test Positive} \cap \text{Infected})}{P(\text{Test Positive})} \]
\[ = \frac{.01}{.011} \approx .909 \]
**Answer:** The probability that the person is infected given a positive test is approximately **90.9%**.
---
## Part b) - Probability the test yields a positive result in the community
### Given Data:
| | Test Positive | Test Negative | Total Prob |
|--------------------------|-----------------|-----------------|------------|
| **Infected** | .01 | .2 | .21 |
| **Not Infected** | .001 | .5 | .501 |
| **Total Prob** | .011 | .7 | 1. |
### Calculation:
\[ P(\text{Test Positive}) = .011 \]
**Answer:** The probability that the test yields a positive result in the community is **1.1%** (or .011).
---
**Summary:**
- The probability that a person with a positive test is actually infected is approximately **90.9%**.
- The overall probability that the test is positive in the community is **1.1%**.
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