Question

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
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. 15%
b. about 94%
c. 75%
d. 20%

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. Here, event $A$ is taking Japanese and event $B$ is being in the anime club.

Step2: Identify values from the table

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

Step3: Calculate the conditional probability

$P(A|B)=\frac{0.15}{0.16}=\frac{15}{16}= 0.9375\approx94\%$

Answer:

B. About 94%