If `P(A)=(2)/(3), P(B)=(2)/(5) and P(A cup B)-P(A cap B)=(2)/(5)` then what is `P(A cap B)` equal to?

Options

A. `(3)/(5)`
B. `(5)/(11)`
C. `(1)/(3)`
D. None of these

Answer

B

Explanation

`P(A cup B)-P(A cap B)=(2)/(5)`
We know that `P(A cup B)-P(A)+P(B)=P(A cap B)`
`therefore P(A)+P(B)-P(A capB)-P(A capB)=(2)/(5)`
`(2)/(3)+(2)/(5)-2P(A cap B)=(2)/(5)`
`-2P(A cap B)=(2)/(5)-(2)/(3)-(2)/(5)`
`-2P(A cap B)=(6-16)/(15)=-(2)/(3)xx(-1)/(2)=(1)/(3)`