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 who plays a sport does not play an instrument?

	plays a sport	does not play a sport
does not play an instrument	7	10

Explanation:

Step1: Identify total students who play a sport

To find the total number of students who play a sport, we add the number of students who play a sport and play an instrument, and those who play a sport and do not play an instrument. So, $5 + 7 = 12$.

Step2: Identify students who play a sport and do not play an instrument

From the table, the number of students who play a sport and do not play an instrument is $7$.

Step3: Calculate the probability

The probability is the number of favorable outcomes (students who play a sport and do not play an instrument) divided by the number of total outcomes (students who play a sport). So, the probability is $\frac{7}{12}$.

Answer:

$\frac{7}{12}$