A and B are two independent events such that `P(A)=(1)/(5), P(A cup B)=(7)/(10). " Then ", P(overline(B))`=

Options

A. `(2)/(7)`
B. `(3)/(7)`
C. `(3)/(8)`
D. `(7)/(9)`

Answer

B

Explanation

As, A and B are independent event
`P(A cap B)=(1)/(5)P(B)`
Now, `P(A cup B)=P(A)+P(B)-P(A cap B)`
`(7)/(10)=(1)/(5)+P(B)-(1)/(5)P(B)`
`P(B)(1-(1)/(5))=(7)/(10)-(1)/(5)`
Now,`P(overset(_)B)=1-P(B)=1-(5)/(8)=(3)/(8)`