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 [tex]x[/tex], the number of students who play both instruments is
[tex]\dfrac{5x}{100}=\dfrac{x}{20}[/tex]
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 [tex]100-21 = 79[/tex]
d) By the same logic, the probability of V is [tex]13+5=18[/tex] percent. So, we have
[tex]P(N\cup V) = P(N)+P(V)-P(N\cap V) = 0.21+0.18-0.05=0.34[/tex]
e) We have
[tex]P(\lnot N \cap \lnot V) = P(\lnot(N\cup V))[/tex]
And we just computed the probability of [tex]N\cup V[/tex] to be 0.34. So, we have
[tex]P(\lnot(N\cup V))=1-0.34=0.66[/tex]
