From science to arts, IDNLearn.com has the answers to all your questions. Join our Q&A platform to access reliable and detailed answers from experts in various fields.
Sagot :
To determine the likelihood that a student takes Japanese given that they are in the anime club, we need to calculate the conditional probability. Specifically, we seek \( P(\text{Take Japanese} \mid \text{In Anime Club}) \).
Based on the given table:
- The proportion of students who take Japanese and are in the anime club is \( P(\text{Take Japanese and In Anime Club}) = 0.13 \).
- The proportion of students who are in the anime club is \( P(\text{In Anime Club}) = 0.14 \).
The conditional probability \( P(\text{Take Japanese} \mid \text{In Anime Club}) \) is given by the following formula:
[tex]\[ P(\text{Take Japanese} \mid \text{In Anime Club}) = \frac{P(\text{Take Japanese and In Anime Club})}{P(\text{In Anime Club})} \][/tex]
Substituting the given values:
[tex]\[ P(\text{Take Japanese} \mid \text{In Anime Club}) = \frac{0.13}{0.14} \][/tex]
Performing the division:
[tex]\[ P(\text{Take Japanese} \mid \text{In Anime Club}) \approx 0.9285714285714285 \][/tex]
Converting this to a percentage:
[tex]\[ 0.9285714285714285 \times 100 \approx 92.85714285714285\% \][/tex]
Therefore, the likelihood that a student takes Japanese given that they are in the anime club is about 93%.
Thus, the correct answer is:
A. About [tex]\( 93\% \)[/tex]
Based on the given table:
- The proportion of students who take Japanese and are in the anime club is \( P(\text{Take Japanese and In Anime Club}) = 0.13 \).
- The proportion of students who are in the anime club is \( P(\text{In Anime Club}) = 0.14 \).
The conditional probability \( P(\text{Take Japanese} \mid \text{In Anime Club}) \) is given by the following formula:
[tex]\[ P(\text{Take Japanese} \mid \text{In Anime Club}) = \frac{P(\text{Take Japanese and In Anime Club})}{P(\text{In Anime Club})} \][/tex]
Substituting the given values:
[tex]\[ P(\text{Take Japanese} \mid \text{In Anime Club}) = \frac{0.13}{0.14} \][/tex]
Performing the division:
[tex]\[ P(\text{Take Japanese} \mid \text{In Anime Club}) \approx 0.9285714285714285 \][/tex]
Converting this to a percentage:
[tex]\[ 0.9285714285714285 \times 100 \approx 92.85714285714285\% \][/tex]
Therefore, the likelihood that a student takes Japanese given that they are in the anime club is about 93%.
Thus, the correct answer is:
A. About [tex]\( 93\% \)[/tex]
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Thank you for visiting IDNLearn.com. We’re here to provide dependable answers, so visit us again soon.