Question

In a class of students, the following data table summarizes how many students play an instrument or a sport. What is the probability that a student does not play a sport given that they play an instrument?
Plays an instrument Does not play an instrument
Plays a sport 9 12
Does not play a sport 4 2

Answer 1

We want P(does not play a sport | plays an instrument) = (number who play an instrument and do not play a sport) / (total who play an instrument) = 4 / (9+4) = 4/13 ≈ 0.3077 (≈30.8%).