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 college’s 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 |\noptions: \\(\frac{51}{100}\\), \\(\frac{39}{80}\\), \\(\frac{13}{17}\\), \\(\frac{39}{100}\\)

the director of health services is concerned about a possible flu outbreak at her college. she surveyed 100 randomly selected residents from the college’s 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 |\noptions: \\(\frac{51}{100}\\), \\(\frac{39}{80}\\), \\(\frac{13}{17}\\), \\(\frac{39}{100}\\)

Answer

: $\frac{13}{17}$

Explanation:

Step1: Identify conditional probability

We need $P(\text{Had Flu Shot} | \text{Male})$, calculated as $\frac{\text{Male with flu shot}}{\text{Total male residents}}$.

Step2: Extract values from table

Male with flu shot = 39, Total male residents = 51.

Step3: Simplify the fraction

$\frac{39}{51} = \frac{13}{17}$ (divide numerator and denominator by 3)