High School

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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?

Residents at College Dormitories:

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

A. [tex]$\frac{13}{17}$[/tex]
B. [tex]$\frac{39}{100}$[/tex]
C. [tex]$\frac{51}{100}$[/tex]

Answer :

We are given that 39 out of 51 male residents received a flu shot. To find the probability that a randomly selected male resident had a flu shot, we use the formula for conditional probability:

[tex]$$
P(\text{Flu Shot} \mid \text{Male}) = \frac{\text{Number of males with flu shot}}{\text{Total number of males}}.
$$[/tex]

Substitute the given values:

[tex]$$
P(\text{Flu Shot} \mid \text{Male}) = \frac{39}{51}.
$$[/tex]

To simplify the fraction, note that both the numerator and denominator are divisible by 3:

[tex]$$
\frac{39 \div 3}{51 \div 3} = \frac{13}{17}.
$$[/tex]

Thus, the probability that a dormitory resident chosen at random has had a flu shot, given that he is male, is

[tex]$$
\frac{13}{17}.
$$[/tex]

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