`A` and `B` are events of an experiment such that `0 lt P(A)`, `P(B) lt 1`. If `P(B') gt P(A')`, then

Options

A. `P(AnnB') lt P(A'nnB)`
B. `P(AnnB') = P(A'nnB)`
C. `P(B//A) lt P(A//B)`
D. `P(B//A) gt P(A//B)`

Answer

C

Explanation

`(c )` Given `P(B') gt P(A')`
`impliesP(B) lt P(A)`
`impliesP(A)=P(AnnB')+P(AnnB) gt P(B)`
`=P(A'nnB)+P(AnnB)`
`impliesP(AnnB') gt P(A'nnB)`
`implies(A)` is false and so is `(B)`
`P(B//A)=(P(AnnB))/(P(A)) lt (P(AnnB))/(P(B))=P(A//B)` `:' (c )` is true