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	15	8

Explanation:

Step1: Find total number of students

First, we sum up all the values in the table. The values are 3, 2, 15, and 8. So total students = \(3 + 2 + 15 + 8\) = \(28\).

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 8.

Step3: Calculate probability

Probability is the number of favorable outcomes (students who play neither) divided by total number of outcomes (total students). So probability = \(\frac{8}{28}\) = \(\frac{2}{7}\).

Answer:

\(\frac{2}{7}\)