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.



Circles B and T intersect. Circle B contains 24, circle T contains 31, and the intersection contains 9. Number 14 is outside of the circles.

Given that a randomly chosen student participates in band, what is the probability that the student also participates in track?

StartFraction 9 Over 40 EndFraction
StartFraction 9 Over 33 EndFraction
StartFraction 24 Over 33 EndFraction
StartFraction 31 Over 40 EndFraction

Answer 1

Circle B has 24 only-in-band plus 9 in the intersection, so 33 students participate in band. Of those, 9 also do track. So the probability is 9/33 (which simplifies to 3/11).