the director of health services is concerned about a possible flu outbreak at her college. she surveyed 100…

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?\nresidents at college dormitories\n| |male|female|total|\n|--|--|--|--|\n|had flu shot|39|41|80|\n|didnt have flue shot|12|8|20|\n|total|51|49|100|

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?\nresidents at college dormitories\n| |male|female|total|\n|--|--|--|--|\n|had flu shot|39|41|80|\n|didnt have flue shot|12|8|20|\n|total|51|49|100|

Answer

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 counts, if $A$ is the event of having a flu - shot and $B$ is the event of being male, $P(A|B)=\frac{n(A\cap B)}{n(B)}$, where $n(A\cap B)$ is the number of males who had a flu shot and $n(B)$ is the number of males.

Step2: Identify the relevant values from the table

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

Step3: Calculate the probability

$P=\frac{39}{51}=\frac{13}{17}\approx0.765$

Answer:

$\frac{13}{17}$