College

We appreciate your visit to 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. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

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

A. [tex]$\frac{13}{17}$[/tex]
B. [tex]$\frac{39}{80}$[/tex]
C. [tex]$\frac{39}{100}$[/tex]
D. [tex]$\frac{51}{100}$[/tex]

Answer :

To find the probability that a dormitory resident chosen at random from this group has had a flu shot, given that he is male, we need to focus on the male residents who had a flu shot and the total number of male residents surveyed.

Here's how to solve the problem step by step:

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

2. Identify the total number of male residents surveyed.
- The total number of male residents surveyed is 51.

3. Calculate the probability.
- The probability that a dormitory resident chosen at random from this group has had a flu shot, given that he is male, is the number of males who had a flu shot divided by the total number of males surveyed.
- So, the probability is calculated as [tex]\( \frac{39}{51} \)[/tex].

4. Simplify the fraction.
- Simplifying [tex]\( \frac{39}{51} \)[/tex] gives us approximately 0.7647.

Thus, the probability that a randomly chosen male resident has had a flu shot is approximately 0.765, or [tex]\( \frac{13}{17} \)[/tex] in simplified fractional form.

Thanks for taking the time to read 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. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada