In a class 23 of students, 10 play an instrument and 15 play a sport. There are 7 students who play an instrument and also play a sport. What is the probability that a student does not play a sport given that they play an instrument?

The probability that a student does not play a sport given but they play an instrument is 3/23

Step-by-step explanation:

Total students in a class = 23

Students who play sports = 15

Students who play instruments = 10

Students who play both = 7

Probability that a student play sports = 15/23

Probability that a student play instruments = 10/23

Probability that a student play both = 7/23

Probability that a student does not play a sport given but they play an instrument = probability that a student play instruments - Probability that a student play both

= (10-7) / 23

= 3/23

The probability that a student does not play a sport given but they play an instrument is 3/23