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Answer :
To determine the probability that a dormitory resident chosen at random has had a flu shot, given that he is male, let’s follow these steps:
1. Identify the Total Number of Males:
From the table, the total number of males is 51.
2. Identify the Number of Males Who Had a Flu Shot:
From the table, the number of males who had a flu shot is 39.
3. Calculate the Probability:
The probability that a randomly chosen male dormitory resident has had a flu shot is given by the ratio of the number of males who received the flu shot to the total number of males.
[tex]\[ \text{Probability} = \frac{\text{Number of males who had a flu shot}}{\text{Total number of males}} \][/tex]
Plug in the values:
[tex]\[ \text{Probability} = \frac{39}{51} \][/tex]
4. Simplify the Fraction:
Simplifying [tex]\(\frac{39}{51}\)[/tex]:
[tex]\[ \frac{39 \div 3}{51 \div 3} = \frac{13}{17} \][/tex]
So, the simplified probability that a dormitory resident chosen at random has had a flu shot, given that he is male, is [tex]\(\frac{13}{17}\)[/tex].
Therefore, the correct answer is:
[tex]\[ \frac{13}{17} \][/tex]
1. Identify the Total Number of Males:
From the table, the total number of males is 51.
2. Identify the Number of Males Who Had a Flu Shot:
From the table, the number of males who had a flu shot is 39.
3. Calculate the Probability:
The probability that a randomly chosen male dormitory resident has had a flu shot is given by the ratio of the number of males who received the flu shot to the total number of males.
[tex]\[ \text{Probability} = \frac{\text{Number of males who had a flu shot}}{\text{Total number of males}} \][/tex]
Plug in the values:
[tex]\[ \text{Probability} = \frac{39}{51} \][/tex]
4. Simplify the Fraction:
Simplifying [tex]\(\frac{39}{51}\)[/tex]:
[tex]\[ \frac{39 \div 3}{51 \div 3} = \frac{13}{17} \][/tex]
So, the simplified probability that a dormitory resident chosen at random has had a flu shot, given that he is male, is [tex]\(\frac{13}{17}\)[/tex].
Therefore, the correct answer is:
[tex]\[ \frac{13}{17} \][/tex]
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