We appreciate your visit to The director of health services is concerned about a possible flu outbreak at her college She surveyed 100 randomly selected residents from the college s. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
We begin by identifying the total number of males and the number of males who received a flu shot from the table. The table tells us that there are 51 male residents in total and that 39 of these males had a flu shot.
The probability that a dormitory resident has had a flu shot, given that he is male, is calculated using the formula for conditional probability:
[tex]$$
P(\text{Flu Shot} \mid \text{Male}) = \frac{\text{Number of males with a flu shot}}{\text{Total number of males}}.
$$[/tex]
Substituting the numbers from the table, we have:
[tex]$$
P(\text{Flu Shot} \mid \text{Male}) = \frac{39}{51}.
$$[/tex]
This fraction simplifies by dividing both the numerator and the denominator by their greatest common divisor, which is 3:
[tex]$$
\frac{39 \div 3}{51 \div 3} = \frac{13}{17}.
$$[/tex]
Thus, the probability that a dormitory resident chosen at random has had a flu shot, given that he is male, is:
[tex]$$
\boxed{\frac{13}{17}}.
$$[/tex]
The probability that a dormitory resident has had a flu shot, given that he is male, is calculated using the formula for conditional probability:
[tex]$$
P(\text{Flu Shot} \mid \text{Male}) = \frac{\text{Number of males with a flu shot}}{\text{Total number of males}}.
$$[/tex]
Substituting the numbers from the table, we have:
[tex]$$
P(\text{Flu Shot} \mid \text{Male}) = \frac{39}{51}.
$$[/tex]
This fraction simplifies by dividing both the numerator and the denominator by their greatest common divisor, which is 3:
[tex]$$
\frac{39 \div 3}{51 \div 3} = \frac{13}{17}.
$$[/tex]
Thus, the probability that a dormitory resident chosen at random has had a flu shot, given that he is male, is:
[tex]$$
\boxed{\frac{13}{17}}.
$$[/tex]
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