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 the context of this problem, let $A$ be the event of having a flu - shot and $B$ be the event of being male. We can also use the formula $P(A|B)=\frac{n(A\cap B)}{n(B)}$, where $n(A\cap B)$ is the number of elements in the intersection of $A$ and $B$, and $n(B)$ is the number of elements in $B$.

Step2: Identify the relevant values from the table

The number of males who had a flu - shot $n(A\cap B) = 39$, and the total number of males $n(B)=51$.

Step3: Calculate the probability

$P(\text{had flu - shot}|\text{male})=\frac{39}{51}=\frac{13}{17}\approx0.765$

Answer:

$\frac{13}{17}$