To determine the probability of a false positive given that the test result is positive, we will follow these steps.
1. Understand the table and the definitions:
- A false positive occurs when the test is positive but the disease is absent.
- We need to find the probability of having a false positive (disease absent and test positive) given that the test result is positive.
2. Identify relevant values from the table:
- The number of cases where the test is positive and the disease is absent (false positives): 37
- The total number of positive test results: 247
3. Using the identified values, compute the probability:
- The probability of a false positive given that the test is positive would be the ratio of false positives to the total number of positive tests.
[tex]\[
\text{Probability of a false positive} = \frac{\text{Number of false positives}}{\text{Total positive tests}} = \frac{37}{247}
\][/tex]
4. Conclusion:
- Therefore, the probability of a false positive given that the test is positive is:
[tex]\[
\frac{37}{247} \approx 0.1498 \text{ or } 14.98\%
\][/tex]
This means there is approximately a 14.98% chance that a positive test result is a false positive.
