Question

In a certain Algebra 2 class of 29 students, 5 of them play basketball and 16 of them play baseball. There are 10 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?

Answer 1

ANSWER

`P(both\:sports)= (2)/(29)`

Step-by-step explanation
Let the number who plays both games be

`x`
Then those who play only basketball

`= 5 - x`

and those who play only baseball

`= 16 - x`

We were given that 10 students play neither sports.

We can then write the following equation,


`(5 - x) + x + (16 - x) + 10 = 29`

This implies that,


`- x + x - x = 29 - 5 - 16 - 10`

This simplifies to,


`- x = - 2`

This gives us,


`x = 2`

Therefore the number of students play both basketball and baseball is 2.

The probability that a student chosen from the class plays both basketball and baseball ball


`= (2)/(29)`