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?

	male	female	total
didnt have flue shot	12	8	20
total	51	49	100

residents at college dormitories

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of the table, if $A$ is the event of having a flu - shot and $B$ is the event of being male, $P(A|B)=\frac{\text{Number of males who had flu shot}}{\text{Total number of males}}$.

Step2: Identify relevant values from the table

The number of males who had a flu shot is 39, and the total number of males is 51.

Step3: Calculate the probability

$P=\frac{39}{51}=\frac{13}{17}$

Answer:

$\frac{13}{17}$