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 …

Question

asked Jul 2, 2019 164k views

2 Answers

Ximmyxiao · Answer 1 · 2019-07-07T03:45:43+0000

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)=
(6)/(15)

=
(2)/(5)

Probability of student chosen playing violin =

P(V)=
(4)/(15)

=
(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,

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

$P(V\cup P)=(4)/(15)+(2)/(5)-0$

$P(V\cup P)=(4)/(15)+(2)/(5)$

$P(V\cup P)=(4+6)/(15)$

$P(V\cup P)=(10)/(15)$

$P(V\cup P)= 0.666$

= 0.67

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