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?\n\nresidents at college dormitories\n| | male | female | total |\n|--|--|--|--|\n| had flu shot | 39 | 41 | 80 |\n| didnt have flu 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?\n\nresidents at college dormitories\n| | male | female | total |\n|--|--|--|--|\n| had flu shot | 39 | 41 | 80 |\n| didnt have flu 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 the context of this problem, let $A$ be the event of having a flu - shot and $B$ be the event of being male. Then $P(A|B)=\frac{n(A\cap B)}{n(B)}$, where $n(A\cap B)$ is the number of males who had a flu - shot and $n(B)$ is the total number of males.

Step2: Identify values from the table

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

$P(A|B)=\frac{39}{51}=\frac{13}{17}\approx0.765$

Answer:

$\frac{13}{17}$