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?

The Venn diagram is not included, so I am going to explain the procedure and you will be able to calculate the result just plugging the numbers.

From Vend diagram you will be able to conclude two numbers:

1) the total number os students surveyed that participate in band (B)

2) the total number of students surveyed that participate in track (T)

3) the total number of students surveyed that participate in both band (B) and track (T) = B∩T

4) ) the total number of students surveyed, which is: total number of students in band B + total number of students in track - less the number of students that participate in both. = B + T - (B∩T)

So, the probability that one student that participate in band (B) also participate in track (T) =

Number of students that participate in both / number of students that participate in band = (B∩T) / B

Now, you just have to find B∩T and B from the diagram and plugg in into the formula (B∩T)/B. That's it.