To calculate the probability that a randomly selected person who tested positive for the flu is vaccinated, we need to use the given information.
We're provided with:
- The total number of people who tested positive for the flu, which is 2,321.
- The number of people who were vaccinated and tested positive for the flu, which is 465.
We need to find the ratio of people who were vaccinated and tested positive to the total number of people who tested positive.
This is given by the formula:
[tex]\[
P(\text{Vaccinated}|\text{Tested Positive}) = \frac{\text{Number of Vaccinated and Tested Positive}}{\text{Total Number of Tested Positive}}
\][/tex]
Substituting the values provided:
[tex]\[
P(\text{Vaccinated}|\text{Tested Positive}) = \frac{465}{2,321}
\][/tex]
After performing the division, we obtain:
[tex]\[
P(\text{Vaccinated}|\text{Tested Positive}) \approx 0.2003446790176648
\][/tex]
Thus, the probability that a randomly selected person who tested positive for the flu is vaccinated is approximately 0.2003 (or about 20.03%).
The correct answer from the given options is:
[tex]\[
\frac{465}{2,321}
\][/tex]
