Question

Need help with this ASAP

Answer 1

a) The diagram shows that 16% of the students plays only the piano, 13% of the students plays only the violin, and 5% of the students plays both instruments.

So, the percentage of students playing the piano is 21%, because you can choose a students who plays only the piano (16%) or a student who plays both instruments (5%)

b) We can't answer this question without knowing the number of students in the school. In fact, we only know that 5% of the students plays both instrument. This means that, if the total number of students is
`x`, the number of students who play both instruments is

`(5x)/(100)=(x)/(20)`

And it is impossible to evaluate this quantity without knowing the value for x.

c) Since the probability of N is 21% (see point a), the probability of not N will be
`100-21 = 79`

d) By the same logic, the probability of V is
`13+5=18` percent. So, we have

`P(N\cup V) = P(N)+P(V)-P(N\cap V) = 0.21+0.18-0.05=0.34`

e) We have

`P(\lnot N \cap \lnot V) = P(\lnot(N\cup V))`

And we just computed the probability of
`N\cup V` to be 0.34. So, we have

`P(\lnot(N\cup V))=1-0.34=0.66`