Answered

Based on this two-way table, what is the probability of a false positive given that the test is positive?

(A false positive means that the test result is positive, but the end result, such as the presence of a disease, is negative.)

[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline & \multicolumn{4}{|c|}{ Test Result } \\
\hline & & Positive & Negative & Total \\
\hline \multirow{3}{*}{ Disease } & Present & 210 & 3 & 213 \\
\hline & Absent & 37 & 113 & 150 \\
\hline & Total & 247 & 116 & 363 \\
\hline
\end{tabular}
\][/tex]

A. [tex]$\frac{210}{247}$[/tex]

B. [tex]$\frac{37}{247}$[/tex]

C. [tex]$\frac{210}{213}$[/tex]

D. [tex]$\frac{37}{150}$[/tex]



Answer :

GinnyAnswer
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.

Other Questions