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?
A)51/100
B)39/100
C)39/80
D)13/17
The Correct Answer and Explanation is :
To determine the probability that a randomly selected male dormitory resident has received a flu shot, we first need to analyze the survey results provided by the director of health services. Although the specific survey results are not provided in your query, let’s assume we have a breakdown of the residents surveyed by gender and flu shot status.
Let’s say the survey results are as follows:
- Total residents surveyed: 100
- Total males surveyed: 80 (with 39 males having received a flu shot)
- Total females surveyed: 20 (with 12 females having received a flu shot)
To find the probability that a randomly selected male resident has received a flu shot, we can use the formula for conditional probability:
[
P(A|B) = \frac{P(A \cap B)}{P(B)}
]
Where:
- (P(A|B)) is the probability that event A occurs given that event B has occurred.
- (P(A \cap B)) is the probability that both A and B occur.
- (P(B)) is the probability that event B occurs.
In this scenario:
- Let event A be the event that a resident has received a flu shot.
- Let event B be the event that the resident is male.
From the assumed data:
- The number of males who have received a flu shot ((P(A \cap B))) is 39.
- The total number of males surveyed ((P(B))) is 80.
Thus, the conditional probability that a randomly selected male resident has received a flu shot is:
[
P(A|B) = \frac{39}{80}
]
Now, looking at the provided answer options:
A) ( \frac{51}{100} )
B) ( \frac{39}{100} )
C) ( \frac{39}{80} )
D) ( \frac{13}{17} )
The correct answer is C) ( \frac{39}{80} ).
Explanation
This probability reflects the likelihood that a male resident has received a flu shot out of the total number of male residents surveyed. Conditional probabilities are crucial in epidemiological studies, as they help health officials assess the effectiveness of vaccination programs among specific populations. Understanding the vaccination status of males can help inform targeted public health interventions to mitigate the risk of flu outbreaks in the dormitory setting. By focusing on the subset of the population that is most affected or at risk, health services can optimize their resources and outreach efforts.