Questions: Fairview High School has an anime (Japanese animation) club that any student can attend. The relative frequency table shows the proportion of students in the high school who take Japanese and/or are in the anime club. Take Japanese Do not take Japanese Total ----------------------------------------------------------------- In anime club 0.15 0.01 0.16 Not in anime club 0.05 0.79 0.84 Total 0.20 0.80 1.0 Given that a student is in the anime club, what is the likelihood that he or she takes Japanese? A. 20% B. 15% C. About 94% D. 75%

Solution Steps

To find the likelihood that a student takes Japanese given that they are in the anime club, we need to use conditional probability. The formula for conditional probability is:

\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]

Where:

• \( P(A|B) \) is the probability of event A occurring given that B has occurred.
• \( P(A \cap B) \) is the probability of both events A and B occurring.
• \( P(B) \) is the probability of event B occurring.

In this case:

• Event A is "taking Japanese".
• Event B is "being in the anime club".

From the table:

• \( P(A \cap B) \) (probability of taking Japanese and being in the anime club) is 0.15.
• \( P(B) \) (probability of being in the anime club) is 0.16.

We can now calculate \( P(A|B) \).

From the relative frequency table, we identify the following probabilities:

• \( P(A \cap B) \) (probability of taking Japanese and being in the anime club) is 0.15.
• \( P(B) \) (probability of being in the anime club) is 0.16.

We use the conditional probability formula: \[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]

Substituting the given values: \[ P(A|B) = \frac{0.15}{0.16} \]

Perform the division to find \( P(A|B) \): \[ P(A|B) = 0.9375 \]

Convert the probability to a percentage: \[ P(A|B) \times 100 = 93.75\% \]

Final Answer