To determine the likelihood that a student who takes Japanese is in the anime club, we need to use the concept of conditional probability. Specifically, we want to find the probability of a student being in the anime club given that the student takes Japanese.
The conditional probability [tex]\( P(A|B) \)[/tex] is given by the formula:
[tex]\[
P(A|B) = \frac{P(A \cap B)}{P(B)}
\][/tex]
Where:
- [tex]\( A \)[/tex] is the event that the student is in the anime club.
- [tex]\( B \)[/tex] is the event that the student takes Japanese.
- [tex]\( P(A \cap B) \)[/tex] is the probability that the student is both in the anime club and takes Japanese.
- [tex]\( P(B) \)[/tex] is the probability that a student takes Japanese.
From the relative frequency table:
- [tex]\( P(A \cap B) = 0.15 \)[/tex], the proportion of students who are both in the anime club and take Japanese.
- [tex]\( P(B) = 0.20 \)[/tex], the proportion of students who take Japanese.
Now, we can use the formula to find the conditional probability:
[tex]\[
P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{0.15}{0.20}
\][/tex]
Simplifying this fraction:
[tex]\[
P(A|B) = \frac{0.15}{0.20} = 0.75
\][/tex]
Therefore, the probability that a student who takes Japanese is in the anime club is 0.75, or 75%.
Given the options:
A. [tex]\( 75 \% \)[/tex]
B. [tex]\( 20 \% \)[/tex]
C. [tex]\( 15 \% \)[/tex]
D. About [tex]\( 94 \% \)[/tex]
The correct answer is [tex]\( \boxed{75\%} \)[/tex].
