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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, we need to focus only on the male residents.
Here's how we can determine this probability:
1. Identify the Total Number of Male Residents: From the table, there are a total of 51 male residents.
2. Identify the Number of Male Residents Who Had a Flu Shot: From the table, 39 male residents received a flu shot.
3. Calculate the Conditional Probability: We want to find the probability that a randomly chosen male resident has had a flu shot. The formula for this conditional probability is:
[tex]\[
P(\text{Had Flu Shot | Male}) = \frac{\text{Number of Males Who Had a Flu Shot}}{\text{Total Number of Male Residents}}
\][/tex]
Substituting the numbers we have:
[tex]\[
P(\text{Had Flu Shot | Male}) = \frac{39}{51}
\][/tex]
4. Calculate the Result: When you divide 39 by 51, the result is approximately 0.7647.
Thus, the probability that a randomly selected male dormitory resident has had a flu shot is approximately 0.765, or 76.47%.
Here's how we can determine this probability:
1. Identify the Total Number of Male Residents: From the table, there are a total of 51 male residents.
2. Identify the Number of Male Residents Who Had a Flu Shot: From the table, 39 male residents received a flu shot.
3. Calculate the Conditional Probability: We want to find the probability that a randomly chosen male resident has had a flu shot. The formula for this conditional probability is:
[tex]\[
P(\text{Had Flu Shot | Male}) = \frac{\text{Number of Males Who Had a Flu Shot}}{\text{Total Number of Male Residents}}
\][/tex]
Substituting the numbers we have:
[tex]\[
P(\text{Had Flu Shot | Male}) = \frac{39}{51}
\][/tex]
4. Calculate the Result: When you divide 39 by 51, the result is approximately 0.7647.
Thus, the probability that a randomly selected male dormitory resident has had a flu shot is approximately 0.765, or 76.47%.
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