Question

at mountain high school, the students were surveyed about their participation in band (b) and track (t). the results of the survey are shown in the venn diagram. given that a randomly chosen student participates in band, what is the probability that the student also participates in track? o $\frac{9}{40}$ o $\frac{9}{33}$ o $\frac{24}{33}$ o $\frac{31}{40}$

Explanation:

Step1: Identify relevant numbers

The number of students in band (B) is \(24 + 9=33\). The number of students in both band and track is \(9\).

Step2: Apply conditional - probability formula

The probability of a student being in track given they are in band is \(P(T|B)=\frac{n(B\cap T)}{n(B)}\), where \(n(B\cap T)\) is the number of students in both band and track and \(n(B)\) is the number of students in band. So \(P(T|B)=\frac{9}{33}\).

Answer:

\(\frac{9}{33}\)