Question

In a certain Algebra 2 class of 26 students, 7 of them play basketballand 13 of them play baseball. There are 10 students who play neithersport. What is the probability that a student chosen randomly from theclass plays both basketball and baseball?

Answer 1

The situation can be represented by the above diagram

7 students play basketball, that is,

x + y = 7 (eq. 1)

13 students play baseball, that is,

y + z = 13 (eq. 2)

10 students who play neither sport.

x + y +z = 26 - 10

x + y +z = 16

Substituting with equation 2,

x + 13 = 16

x = 16 - 13

x = 3

Substituting with equation 1,

3 + y = 7

y = 7 - 3

y = 4

Then there are 4 students that play both sports. Therefore, the probability that a student chosen randomly from the class plays both basketball and baseball is: 4/26 = 2/13