Question

In a class 27 of students, 10 play an instrument and 11 play a sport. There are 13 students who do not play an instrument or a sport. What is the probability that a student does not play an instrument given that they play a sport?

Answer 1

4

Explanation:

Total students = 27

A = students playing instrument

n(A) = 10

B = students playing sport

n(B) = 11

(A∪B)' = students who do not play an instrument or a sport

n(A∪B)' = 13

n(A∪B) = 27 - 13 = 14

n(A∩B) = n(A) + n(B) - n(A∪B)

= 10 + 11 - 14 = 21 - 14

= 7

No. of students playing only instrument = 10 - 7 = 3

No. of students does not play an instrument given that they play a sport = 11 - 7 = 4

P(No. of students does not play an instrument given that they play a sport ) = 4/27