If a and b are two events such that p(aub)=3/4

1) 5/12

2) 3/8

3) 5/8

4) ½

Solution: Option (1) 5/12

Given that, P(AUB) = ¾, P(A∩B) = ¼, P(A’) = ⅔

P(A) = 1-P(A’)

P(A) = 1- (⅔) = ⅓

Hence, P(B) = ⅔

P(A’∩B) = P(B) – P(A∩B)

We know that, P(AUB) = P(A)+P(B) – P(A∩B)

P(B) – P(A∩B) = P(AUB) – P(A)

P(A’∩B) = (¾) – (⅓)

P(A’∩B) = (9-4)/12

P(A’∩B) = 5/12.