For two events `A` and `B`, if `P(A)=P((A)/(B))=(1)/(4)` and `P((B)/(A))=(1)/(2)`, then which of the following is not true ?

Options

A. A and B are mutually exclusive events
B. A and B are independent events such that `P(overline(A)//B)=3//4`
C. A and B are independent events such that `P(overline(A)//B)=1//2`
D. A and B are in independent events such that `P(overline(A)//B)=3//4`

Answer

B

Explanation

We have,
`P(A)=P(A//B)=1//4`
This shows that A and B are independent events.
`therefore P(B)=P(B//A)=1//2`
Now, `P(A//B)=(1)/(4) implies P(overline(A)//B)=1-(1)/(4)=(3)/(4)`
Hence, alternatives (b) is correct.