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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?
A)51 / 100
B)39 / 100
C)39 / 80
D)13 / 17
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Answer
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Step 1: First, we need to determine how many males in the sample of 100 students have had a flu shot.
The problem states that 39 out of the 51 males surveyed had received a flu shot.
Step 2: Now, we need to calculate the probability of choosing a male student who has had a flu shot.
P(\text{Male and Flu Shot}) = \frac{\text{Number of males with flu shot}}{\text{Total number of males}}
To do this, we'll divide the number of males who had a flu shot by the total number of males in the survey. The probability P(Male and Flu Shot) is calculated as:
Final Answer
The probability that a dormitory resident chosen at random from this group is male, given that he has had a flu shot, is \frac{13}{17}.
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