QuestionThe director of health services is concerned about a possible flu outbreak at her college. She surveyed 100 randomiy 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?
Rosidonts At Collego Dormitorios
\begin{tabular}{|c|c|c|c|}
\hline & Male & Female & Total \\
\hline Had Flu Shot & 39 & 41 & 80 \\
\hline \begin{tabular}{c}
Didn't Have \\
Flue Shot
\end{tabular} & 12 & 8 & 20 \\
\hline Total & 51 & 49 & 100 \\
\hline
\end{tabular}
Studdy Solution
STEP 1
1. We are given a table of data showing the number of male and female residents who had or did not have a flu shot.
2. We need to find the probability that a randomly chosen male resident has had a flu shot.
STEP 2
1. Identify the relevant data from the table.
2. Calculate the conditional probability.
STEP 3
Identify the number of male residents who had a flu shot and the total number of male residents.
From the table:
- Number of males who had a flu shot: 39
- Total number of males: 51
STEP 4
Calculate the probability that a randomly chosen male resident has had a flu shot.
The probability is given by:
Substitute the values:
Simplify the fraction:
The probability that a dormitory resident chosen at random from this group has had a flu shot, given that he is male, is:
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