Question

the director of health services is concerned about a possible flu outbreak at her college. she surveyed 100 randomly selected residents from the colleges 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?

	had flu shot	didnt have flu shot	total
female	41	8	49
total	80	20	100

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In the context of a two - way table, if $A$ is the event of being male and $B$ is the event of having a flu shot, $P(A\cap B)$ is the proportion of males who had a flu shot, and $P(B)$ is the proportion of those who had a flu shot.

Step2: Identify values from the table

The number of males who had a flu shot is 39. The total number of people who had a flu shot is 80.

Step3: Calculate the probability

$P(\text{Male}|\text{Flu Shot})=\frac{\text{Number of males with flu shot}}{\text{Total number of people with flu shot}}=\frac{39}{80}$.

Answer:

$\frac{39}{80}$