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
does not play a sport	3	11

Explanation:

Step1: Identify relevant counts

Number of students who play an instrument and do not play a sport: 3; Total students who play an instrument: $8 + 3 = 11$

Step2: Calculate conditional probability

Probability = $\frac{\text{Plays instrument and no sport}}{\text{Plays instrument}} = \frac{3}{11}$

Answer:

$\frac{3}{11}$