Question

A group of 15 students play different instruments, 6 play piano, 4 play violin and 5 play guitar. A student is chosen at random. What is the probability that the student chosen plays violin or piano?

Answer 1

6/15+4/15=10/15 = 2/3

Answer 2

Total number of students playing piano, violin and guitar = 15

Given: 6 students play piano, 4 play violin and 5 play guitar.

Probability of student chosen playing piano =

P(P)= $\frac{6}{15}$

= $\frac{2}{5}$

Probability of student chosen playing violin =

P(V)= $\frac{4}{15}$

= $\frac{4}{15}$

Now, we have to find the probability that the student chosen plays violin or piano.

using the formula,

$P(V\cup P)=P(V)+P(P)-P(V\cap P)$

Since there is no student chosen who plays violin and piano both, therefore $P(V\cap P)=0$.

Now,

$P(V\cup P)=P(V)+P(P)-P(V\cap P)$

$P(V\cup P)=\frac{4}{15}+\frac{2}{5}-0$

$P(V\cup P)=\frac{4}{15}+\frac{2}{5}$

$P(V\cup P)=\frac{4+6}{15}$

$P(V\cup P)=\frac{10}{15}$

$P(V\cup P)= 0.666$

= 0.67

Therefore, the probability that the student chosen plays violin or piano is 0.67.