at mountain high school, the students were surveyed about their participation in band (b) and track (t). the…

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 this problem, let $A$ be the event of participating in track and $B$ be the event of participating in band. Then $P(A|B)=\frac{n(A\cap B)}{n(B)}$, where $n(A\cap B)$ is the number of elements in the intersection of $A$ and $B$, and $n(B)$ is the number of elements in $B$.

Step2: Identify values from the Venn - diagram

From the Venn - diagram, the number of students who participate in both band and track $n(B\cap T)=9$, and the number of students who participate in band $n(B)=24 + 9=33$.

Step3: Calculate the conditional probability

Using the formula $P(T|B)=\frac{n(B\cap T)}{n(B)}$, we substitute $n(B\cap T) = 9$ and $n(B)=33$ to get $P(T|B)=\frac{9}{33}$.

Answer:

$\frac{9}{33}$