Question

the editor of a school magazine polled randomly - selected students in the 8th, 9th, and 10th grades. they were asked which activity they enjoyed the most: watching sports, reading, or listening to music. the two - way frequency table shows the data she collected. based on the data in the table, what is the approximate probability that a randomly selected student is in the 9th grade, given that he or she enjoys watching sports the most? a. 0.39 b. 0.35 c. 0.37 d. 0.33

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In the context of the two - way table, if $A$ is the event that a student is in 9th grade and $B$ is the event that a student enjoys watching sports, then $P(A\cap B)$ is the number of 9th - grade students who watch sports divided by the total number of students, and $P(B)$ is the number of students who watch sports divided by the total number of students. So $P(A|B)=\frac{n(A\cap B)}{n(B)}$, where $n(A\cap B)$ is the frequency of the intersection of the two events and $n(B)$ is the frequency of the conditioning event.

Step2: Identify relevant frequencies from the table

The number of 9th - grade students who watch sports, $n(A\cap B) = 13$. The number of students who watch sports, $n(B)=35$.

Step3: Calculate the probability

$P=\frac{13}{35}\approx0.37$

Answer:

B. 0.37