Question

In a certain Algebra 2 class of 25 students, 13 of them play basketball and 11 of them play baseball. There are 4 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?

Answer 1

`(4)/(5)`

Explanation:

Given: There are 2 classes of 25 students.

13 play basketball

11 play baseball.

4 play neither of sports.

Lets assume basketball as "a" and baseball as "b".

We know, probablity dependent formula; P(a∪b)= P(a)+P(b)-p(a∩b)

As given total number of student is 25

Now, subtituting the values in the formula.

⇒P(a∪b)=
`(13)/(25) +(11)/(25) -(4)/(25)`

taking LCD as 25 to solve.

⇒P(a∪b)=
`(13* 1+11* 1-4* 1)/(25) = (20)/(25)`

∴ P(a∪b)=
`(4)/(5)`

Hence, the probability that a student chosen randomly from the class plays both basketball and baseball is
`(4)/(5)`.