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: $\frac{13}{17}$, $\frac{39}{100}$, $\frac{51}{100}$, $\frac{39}{80}$

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 a contingency table, if \( A \) is "had a flu shot" and \( B \) is "is male", then \( P(A|B) = \frac{\text{Number of males who had flu shot}}{\text{Total number of males}} \).

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

Substitute the values into the formula: \( P(\text{had flu shot} | \text{male}) = \frac{39}{51} \). Simplify the fraction by dividing numerator and denominator by 3: \( \frac{39 \div 3}{51 \div 3} = \frac{13}{17} \).

Answer:

\(\frac{13}{17}\) (corresponding to the first option)