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?

4

Step-by-step 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