Question

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?

	male	female	total
didnt have flue shot	12	8	20
total	51	49	100

residents at college dormitories

options: \\(\frac{13}{17}\\), \\(\frac{51}{100}\\), \\(\frac{39}{80}\\), \\(\frac{39}{100}\\)

Explanation:

Step1: Recall Conditional Probability Formula

The formula for conditional probability is \( P(A|B) = \frac{P(A \cap B)}{P(B)} \). In this case, event \( A \) is "had a flu shot" and event \( B \) is "is male". So we need the number of males who had a flu shot ( \( A \cap B \)) and the total number of males ( \( B \)).

Step2: Identify Values from Table

From the table, the number of males who had a flu shot is 39, and the total number of males is 51.

Step3: Calculate the Probability

Using the formula, \( P(\text{had flu shot} | \text{male}) = \frac{\text{Number of males with flu shot}}{\text{Total number of males}} = \frac{39}{51} \). Simplify \( \frac{39}{51} \) by dividing numerator and denominator by 3: \( \frac{39\div3}{51\div3} = \frac{13}{17} \).

Answer:

\(\frac{13}{17}\)