Question

for a certain class, the following data table compares how many students play an instrument or a sport. what is the probability that a student chosen randomly from the class plays neither a sport nor an instrument?

	plays an instrument	does not play an instrument
does not play a sport	10	3

Explanation:

Step1: Find total number of students

First, we sum up all the values in the table. The values are 5, 4, 10, and 3. So total students $= 5 + 4 + 10 + 3 = 22$.

Step2: Find number of students who play neither

The number of students who play neither a sport nor an instrument is the value in the cell where "Does not play a sport" and "Does not play an instrument" intersect, which is 3.

Step3: Calculate the probability

Probability is the number of favorable outcomes (students who play neither) divided by the total number of students. So probability $= \frac{3}{22}$.

Answer:

$\frac{3}{22}$