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

Explanation:

Step1: Find the number of students who play a sport

The number of students who play a sport is \(5 + 7=12\).

Step2: Find the number of students who play a sport and do not play an instrument

The number of students who play a sport and do not play an instrument is \(7\).

Step3: Calculate the probability

The probability \(P\) that a student who plays a sport does not play an instrument is given by the formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, the number of favorable outcomes (students who play a sport and do not play an instrument) is \(7\), and the total number of outcomes (students who play a sport) is \(12\). So \(P = \frac{7}{12}\).

Answer:

\(\frac{7}{12}\)