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Answer :
We are asked to find the probability that a dormitory resident has had a flu shot given that the resident is male.
Step 1. Identify the number of males in the sample.
From the table, there are 51 males in total.
Step 2. Identify the number of males who had a flu shot.
The table shows that 39 males had a flu shot.
Step 3. Use the formula for conditional probability.
The probability that a resident has had a flu shot given that the resident is male is given by
[tex]$$
P(\text{Flu Shot} \mid \text{Male}) = \frac{\text{Number of males who had flu shot}}{\text{Number of males}} = \frac{39}{51}.
$$[/tex]
Step 4. Simplify the fraction.
Divide both the numerator and the denominator by 3:
[tex]$$
\frac{39 \div 3}{51 \div 3} = \frac{13}{17}.
$$[/tex]
Thus, the probability that a dormitory resident chosen at random from this group has had a flu shot, given that he is male, is
[tex]$$
\boxed{\frac{13}{17}}.
$$[/tex]
In decimal form, this is approximately 0.7647.
Step 1. Identify the number of males in the sample.
From the table, there are 51 males in total.
Step 2. Identify the number of males who had a flu shot.
The table shows that 39 males had a flu shot.
Step 3. Use the formula for conditional probability.
The probability that a resident has had a flu shot given that the resident is male is given by
[tex]$$
P(\text{Flu Shot} \mid \text{Male}) = \frac{\text{Number of males who had flu shot}}{\text{Number of males}} = \frac{39}{51}.
$$[/tex]
Step 4. Simplify the fraction.
Divide both the numerator and the denominator by 3:
[tex]$$
\frac{39 \div 3}{51 \div 3} = \frac{13}{17}.
$$[/tex]
Thus, the probability that a dormitory resident chosen at random from this group has had a flu shot, given that he is male, is
[tex]$$
\boxed{\frac{13}{17}}.
$$[/tex]
In decimal form, this is approximately 0.7647.
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