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If P(A//B)=P(A//B '), then prove that A ...

If `P(A//B)=P(A//B ')`, then prove that `A` and `B` are independent.

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`P(A//B)=P(A//B')`
or `(P(AnnB))/(P(B))=(P(AnnB'))/(1-P(B))=(P(A)-P(AnnB))/(1-p(B))`
`or P(AnnB)[1-P(B)]=P(B).P(A)-P(B).P(AnnB)`
`orP(AnnB)=P(A).P(B)`
Hence, A and B are indipendent.
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