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 independent events
B. `P(A'//B)=(3)/(4)`
C. `P(B' //A)=(1)/(2)``
D. all of the above

Answer

D

Explanation

Clearly,
`P(B//A)=(P(A cap B))/(P(A)) implies (1)/(2)=(P(A cap B))/(1//4) implies P(A cap B)=(1)/(8)`
and, `P(A//B)=(P(A cap B))/(P(B)) implies (1)/(4) =(1//8)/(P(B)) implies P(B)=(1)/(2)`
Clearly, `P(A cap B)=P(A)xxP(B)`
So, A and B are independent events.
`P(A'//B)=1-P(A//B)=1-(1)/(4)=(3)/(4)`
So, option (c ) is correct.
Hence, all options are correct.