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

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?\no $\frac{9}{40}$\no $\frac{9}{33}$\no $\frac{24}{33}$\no $\frac{31}{40}$

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?\no $\frac{9}{40}$\no $\frac{9}{33}$\no $\frac{24}{33}$\no $\frac{31}{40}$

Answer

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: Use conditional - probability formula

The formula for conditional probability (P(T|B)=\frac{P(T\cap B)}{P(B)}). In terms of counts, (P(T|B)=\frac{n(T\cap B)}{n(B)}), where (n(T\cap B) = 9) and (n(B)=33).

Answer:

(\frac{9}{33})