To determine the likelihood that a student in the anime club takes Japanese, we can use the concept of conditional probability.
The probability we are trying to find is denoted as [tex]\( P(\text{Takes Japanese} \mid \text{In anime club}) \)[/tex]. This is read as "the probability that a student takes Japanese given that the student is in the anime club."
Using the formula for conditional probability, we have:
[tex]\[ P(\text{Takes Japanese} \mid \text{In anime club}) = \frac{P(\text{Takes Japanese} \cap \text{In anime club})}{P(\text{In anime club})} \][/tex]
From the given relative frequency table, we know:
- [tex]\( P(\text{Takes Japanese} \cap \text{In anime club}) = 0.15 \)[/tex]
- [tex]\( P(\text{In anime club}) = 0.16 \)[/tex]
Plug these values into the formula:
[tex]\[ P(\text{Takes Japanese} \mid \text{In anime club}) = \frac{0.15}{0.16} \][/tex]
This calculation results in:
[tex]\[ P(\text{Takes Japanese} \mid \text{In anime club}) = 0.9375 \][/tex]
To convert this probability into a percentage, we multiply by 100:
[tex]\[ 0.9375 \times 100 = 93.75 \% \][/tex]
Hence, the likelihood that a student in the anime club takes Japanese is approximately [tex]\( 93.75\% \)[/tex].
So the correct answer is:
C. About [tex]\( 94\% \)[/tex]
