Question

A high school has 35 students who play only stringed instruments,

10 students who play only brass instruments, 5 students who play
both, and 5 students who don't play either. What is the probability
that a randomly selected student at this high school plays a stringed
instrument or a brass instrument?

Answer 1

`(10)/(11)`

Explanation:

Note : the total number of students is 55

___________________________

`p\left( A\cup B\right) =p\left( A\right) +p\left( B\right) -p\left( A\cap B\right)`

p(A) = 40/55

p(B) = 15/55

`p\left( A\cap B\right) =(5)/(55)`

Therefore,

`p\left( A\cup B\right) =p\left( A\right) +p\left( B\right) -p\left( A\cap B\right)`

`=(40)/(55) +(15)/(55) -(5)/(55)`

`=(50)/(55)`

`=(10)/(11)`