Question

In a certain Algebra 2 class of 30 students, 12 of them play basketball and 17 of them

play baseball. There are 5 students who play neither sport. What is the probability
that a student chosen randomly from the class plays both basketball and baseball?

Answer 1

The probability of students playing both basketball and baseball =
`(2)/(15)`

Explanation:

Total strength of class = 30 students

Number of students who play basketball = 12

Number of students who play baseball = 17

Number of students who play neither sport = 5

Number of students that play either sport =
`30-5` = 25

Number of students who play both sports will be given as:

⇒ Number of students playing basketball + Number of students playing baseball - Number of students playing either

⇒
`12+17-25`

⇒
`4`

Thus probability of students playing both basketball and baseball is given as:

⇒
`(Number\ of\ students\ playing\ both)/(Total\ number\ of\ students)`

⇒
`(4)/(30)`

Dividing numerator and denominator by 2 to reduce to simplest fraction.

⇒
`(4/ 2)/(30/ 2)`

⇒
`(2)/(15)` (Answer)