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

Options

A. `1//3`
B. `2//3`
C. `1//9`
D. `2//9`

Answer

B

Explanation

`"Give "P(A cup B)=(3)/(4),P(A cap B)=(1)/(4)`
`P(overset(_)A)=(2)/(3) Rightarrow P(A)=(1)/(3)`
As we know
`P(A cup B)=P(A)+P(B)-P(Acap B)`
`therefore (3)/(4)=(1)/(3)+P(B)-(1)/(4)`
`Rightarrow (3)/(4)+(1)/(4)-(1)/(3)=P(B)`
`Rightarrow P(B)=(2)/(3)`