If A and B are two events such that `P(A cup B)=(3)/(4)` `P(A cap B)=(1)/(4) and `P(overset(_)A)=(2)/(3)` then what is P(B) equal to?

Options

A. `(1)/(3)`
B. (2)/(3)`
C. `(1)/(8)`
D. `(2)/(9)`

Answer

B

Explanation

`P(A cup B)=(3)/(4)`
`P(A cap B)=(1)/(4)`
`P(overset(_)A)=(2)/(3),P(A)=(1)/(3)`
`therefore P(B)=(3)/(4)-(1)/(3)+(1)/(4)=(9-4+3)/(12)=(8)/(12)=(2)/(3)`
`therefore ` Option (b) is correct