In a class 19 of students, 7 play an instrument and 13 play a sport. there are 4 students who do not play an instrument or a sport. what is the probability that a student who plays an instrument also plays a sport?

Step-by-step explanation:

7+13=20total

4/20=1/5 not sure though

5/7 ≈ 71.4%

Step-by-step explanation:

There are 19 students total.  4 of them do not play an instrument or a sport.  Which means there are 15 students who play either an instrument and/or a sport.

Let's say:

x is the number of students who only play instruments

y is the number of students who play both instruments and sports

z is the number of students who only play sports.

We can use the information to write three equations:

x + y = 7

y + z = 13

x + y + z = 15

Solve the system of equations with either substitution or elimination.  Using elimination, add the first two equations:

x + 2y + z = 20

Subtract the third equation:

y = 5

Therefore, x = 2 and z = 8.

So the percent of students who play an instrument who also play a sport is:

y / (x + y)

5 / (2 + 5)

5/7

≈ 71.4%

b. 153 students do not participate in sports and seventy-five 12th graders were surveyed