Question

In a certain group of 47 students, 16 are taking choir, 17 are taking band, and 7 are taking both. What is the probability that a randomly chosen student is taking choir or band?

Answer 1

We are being asked about the probability of randomly choosing a student that is taken choir or band. It is important to notice that this also includes students that are taking both. Then, the probability we are looking for is given by the sum of the probabilities of choosing a student that takes choir, a student that takes band and a student that takes both. These probibilities are given by the number of students taking those things divided by the total amount of students, 47. Then:

`P=(16)/(47)+(17)/(47)+(7)/(47)=(16+17+7)/(47)=(40)/(47)=0.851`

Multiplying this number by 100 we find the probability written as a percentage:

`0.851\cdot100=85.1`

So there is a 85.1% probability that a randomly chosen stundent is taking choir or band.