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The two-way table shows the results of a recent study on the effectiveness of the flu vaccine.

\begin{tabular}{|c|c|c|c|}
\cline{2-4}
& Pos. & Neg. & Total \\
\hline Vaccinated & 465 & 771 & 1,236 \\
\hline \begin{tabular}{c} Not \\ Vaccinated \end{tabular} & 485 & 600 & 1,085 \\
\hline Total & 950 & 1,371 & 2,321 \\
\hline
\end{tabular}

What is the probability that a randomly selected person who tested positive for the flu is vaccinated?

A. [tex]$\frac{465}{2,321}$[/tex]

B. [tex]$\frac{465}{1,236}$[/tex]

C. [tex]$\frac{465}{950}$[/tex]

D. [tex]$\frac{465}{485}$[/tex]

Sagot :

GinnyAnsweridn
To find the probability that a randomly selected person who tested positive for the flu is vaccinated, we need to use the following information from the table:

- The number of people who tested positive and were vaccinated.
- The total number of people who tested positive.

From the table, we see the following:

- The number of people who tested positive for the flu and were vaccinated is [tex]\(465\)[/tex].
- The total number of people who tested positive for the flu (both vaccinated and not vaccinated) is [tex]\(950\)[/tex].

The probability that a person who tested positive for the flu is vaccinated is given by the ratio of the number of vaccinated positive cases to the total number of positive cases. Therefore, the probability is calculated as follows:

[tex]\[ \frac{\text{Number of vaccinated positive cases}}{\text{Total number of positive cases}} = \frac{465}{950} \][/tex]

So the correct answer is:

[tex]\[ \frac{465}{950} \][/tex]
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