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? \\(\frac{9}{40}\\) \\(\frac{9}{33}\\) \\(\frac{24}{33}\\) \\(\frac{31}{40}\\)

Explanation:

Step1: Identify total in band

To find the total number of students in band (B), we add the number of students only in band and those in both band and track. So, \(24 + 9 = 33\).

Step2: Identify number in both

The number of students in both band and track is \(9\).

Step3: Calculate conditional probability

The conditional probability \(P(T|B)\) is the number of students in both divided by the total number of students in band. So, \(P(T|B)=\frac{9}{33}\).

Answer:

\(\frac{9}{33}\) (corresponding to the option: \(\boldsymbol{\frac{9}{33}}\))