Question

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?

Male
Female
Total
Had Flu Shot
39
41
80
Didn't Have
Flue Shot
12
8
20
Total
51
49
100
Residents At College Dormitories
39
80
39
100
13
17
51
100

Answer 1

To find the probability that a randomly selected male dormitory resident has had a flu shot, we can use the data provided.

First, we summarize the relevant information:

- Total male residents: 51
- Males who had a flu shot: 39
- Males who didn't have a flu shot: 12

Next, we can calculate the probability that a randomly selected male has had a flu shot using the formula for conditional probability:

\[
P(\text{Flu Shot} | \text{Male}) = \frac{P(\text{Flu Shot and Male})}{P(\text{Male})}
\]

In this case, since we are only interested in the male group, we can simplify that to:

\[
P(\text{Flu Shot} | \text{Male}) = \frac{\text{Number of males who had a flu shot}}{\text{Total number of males}} = \frac{39}{51}
\]

Calculating that gives:

\[
P(\text{Flu Shot} | \text{Male}) = \frac{39}{51} \approx 0.7647
\]

Therefore, the probability that a randomly selected male dormitory resident has had a flu shot is approximately **0.765** or **76.5%**.