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Answer :
To find the probability that a dormitory resident chosen at random from this group has had a flu shot, given that he is male, follow these steps:
1. Identify the Relevant Group: Since we are looking for the probability given that the person is male, we are only concerned with the male residents.
2. Determine the Total Number of Males: According to the data, there are a total of 51 male residents.
3. Find the Number of Males Who Had a Flu Shot: From the data, the number of male residents who received a flu shot is 39.
4. Calculate the Conditional Probability: The probability that a randomly chosen male has had a flu shot is calculated by dividing the number of males who had a flu shot by the total number of males.
[tex]\[
\text{Probability} = \frac{\text{Number of males who had a flu shot}}{\text{Total number of males}} = \frac{39}{51}
\][/tex]
5. Simplify the Fraction: When calculated, this fraction simplifies to approximately [tex]\(0.76\)[/tex], or in decimal form, the probability is [tex]\(0.7647\)[/tex].
Therefore, the probability that a dormitory resident chosen at random is male and has had a flu shot is approximately [tex]\(0.7647\)[/tex], which can be expressed as the fraction [tex]\(\frac{13}{17}\)[/tex].
1. Identify the Relevant Group: Since we are looking for the probability given that the person is male, we are only concerned with the male residents.
2. Determine the Total Number of Males: According to the data, there are a total of 51 male residents.
3. Find the Number of Males Who Had a Flu Shot: From the data, the number of male residents who received a flu shot is 39.
4. Calculate the Conditional Probability: The probability that a randomly chosen male has had a flu shot is calculated by dividing the number of males who had a flu shot by the total number of males.
[tex]\[
\text{Probability} = \frac{\text{Number of males who had a flu shot}}{\text{Total number of males}} = \frac{39}{51}
\][/tex]
5. Simplify the Fraction: When calculated, this fraction simplifies to approximately [tex]\(0.76\)[/tex], or in decimal form, the probability is [tex]\(0.7647\)[/tex].
Therefore, the probability that a dormitory resident chosen at random is male and has had a flu shot is approximately [tex]\(0.7647\)[/tex], which can be expressed as the fraction [tex]\(\frac{13}{17}\)[/tex].
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