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

$\dfrac{5x}{100}=\dfrac{x}{20}$

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

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