Question

In a certain class there are 21 students in subject A, 17 in subject B and 10 in subject C. Of these 12 attend subjects A and B, 5 attend subjects B and C, 6 attend subjects A and C. These include 2 students who attend all the three subjects. Find the probability that a student studies one subject alone.

Answer 1

Given, n(A) = 21, n(B) = 17 and n(C) = 10
n(A and B) = 12 , n(B and C) = 6 and n(A and C) = 5
n(A and B and C) = 2
So, n(u) = n(A) + n(B) + n(C) - n(A and B) - n(B and C) - n(A and C) + n( A and B and C)
= 21 + 17 + 10 - 12 - 6 - 5 + 2 = 27

Now, n(only A) = n(A) - n(A and B) - n(A and C) + n(A and B and C)
= 21 - 12 - 6 + 2 = 5
similarly , n(B) = 17 - 12 - 5 + 2 = 2
n(C) = 10 - 6 - 5 + 2 = 1

Now, probability of a student studies one subject alone = {n(only A) + n(only B) + n( only C) }/n(u)
= (5 + 2 + 1)/27 = 8/27