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The director of health services is concerned about a possible flu outbreak at her college. She surveyed 100 randomly selected residents from the college's dormitories to see whether they had received a preventative flu shot. The results are shown below.

What is the probability that a dormitory resident chosen at random from this group has had a flu shot, given that he is male?

[tex]
\[
\begin{tabular}{|c|c|c|c|}
\hline
& \text{Male} & \text{Female} & \text{Total} \\
\hline
\text{Had Flu Shot} & 39 & 41 & 80 \\
\hline
\begin{tabular}{c}
\text{Didn't Have} \\
\text{Flu Shot}
\end{tabular} & 12 & 8 & 20 \\
\hline
\text{Total} & 51 & 49 & 100 \\
\hline
\end{tabular}
\]
[/tex]

A. [tex]\(\frac{39}{80}\)[/tex]

B. [tex]\(\frac{51}{100}\)[/tex]

C. [tex]\(\frac{13}{17}\)[/tex]

D. [tex]\(\frac{39}{100}\)[/tex]

Answer :

To find the probability that a randomly chosen male dormitory resident has had a flu shot, we need to focus on the information provided in the data table specific to the male residents.

Here's how we calculate it step-by-step:

1. Identify the number of male residents who received a flu shot: According to the table, 39 males received a flu shot.

2. Identify the total number of male residents: The table also shows that there are 51 male residents in total.

3. Calculate the probability: The probability that a randomly selected male resident has received a flu shot is given by the ratio of male residents who had the shot to the total number of male residents.

[tex]\[
\text{Probability} = \frac{\text{Number of males with flu shot}}{\text{Total number of males}} = \frac{39}{51}
\][/tex]

4. Simplify the fraction: The fraction [tex]\(\frac{39}{51}\)[/tex] can be simplified if needed, but in this case, the probability as a decimal is approximately 0.7647, or 76.47%.

Therefore, the probability that a randomly chosen dormitory resident is male and has had a flu shot is approximately 0.7647, or 76.47%.

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