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Answer :
To solve this problem, we need to find the probability that a dormitory resident chosen at random is male and has had a flu shot.
Here is how we can approach it step-by-step:
1. Identify the total number of males surveyed: According to the data provided, the total number of male residents surveyed is 51.
2. Identify the number of males who have had a flu shot: The data also tells us that 39 males have had a flu shot.
3. Compute the probability: To find the probability that a randomly chosen male has had a flu shot, we need to divide the number of males who have had the flu shot by the total number of males surveyed.
Mathematically, this can be expressed as:
[tex]\[
\text{Probability} = \frac{\text{Number of males who had a flu shot}}{\text{Total number of males}}
\][/tex]
Substituting the values we have:
[tex]\[
\text{Probability} = \frac{39}{51}
\][/tex]
4. Calculate the result: Simplifying [tex]\(\frac{39}{51}\)[/tex] gives us approximately 0.765.
So, the probability that a dormitory resident chosen at random from this group has had a flu shot, given that he is male, is approximately 0.765 or [tex]\(\frac{13}{17}\)[/tex] when expressed as a fraction.
Here is how we can approach it step-by-step:
1. Identify the total number of males surveyed: According to the data provided, the total number of male residents surveyed is 51.
2. Identify the number of males who have had a flu shot: The data also tells us that 39 males have had a flu shot.
3. Compute the probability: To find the probability that a randomly chosen male has had a flu shot, we need to divide the number of males who have had the flu shot by the total number of males surveyed.
Mathematically, this can be expressed as:
[tex]\[
\text{Probability} = \frac{\text{Number of males who had a flu shot}}{\text{Total number of males}}
\][/tex]
Substituting the values we have:
[tex]\[
\text{Probability} = \frac{39}{51}
\][/tex]
4. Calculate the result: Simplifying [tex]\(\frac{39}{51}\)[/tex] gives us approximately 0.765.
So, the probability that a dormitory resident chosen at random from this group has had a flu shot, given that he is male, is approximately 0.765 or [tex]\(\frac{13}{17}\)[/tex] when expressed as a fraction.
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