Question

A and B are two events such that `P(A cup B)=(3)/(4), P(A)=(1)/(3), P(overline(A) cap B)=`
A. `(5)/(12)`
B. `(3)/(8)`
C. `(5)/(8)`
D. `(1)/(4)`

Answer 1

Correct Answer - A
Since A and `overset(A) cap B` are mutually exclusive events such that
`A cup B= A cup (overline(A) cap B)`
`implies P(A cup B)=P(A)+P(overline(A) cap B)`
`implies (3)/(4)=(1)/(3)+P(overline(A) cap B) implies P(overline(A) cap B)=(5)/(12)`