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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 `Aa n dB` 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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CENGAGE-PROBABILITY II-JEE Advanced Previous Year
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  7. Let X and Y be two events such that P(X)=1/3, P(X|Y)=1/2and P(Y|X)=2/5...

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  8. A signal which can be green or red with probability 4/5 and 1/5 respec...

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  9. Four persons independently solve a certain problem correctly with proa...

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  10. A computer producing factory has only two plants T(1) and T(2). Plant ...

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  11. Let E and F be two independent events. The probability that exactly on...

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  13. Let X and Y be two events such that P(X)=1/3, P(X|Y)=1/2and P(Y|X)=2/5...

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