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Can P[A | (A intersection B) ] be written as below? (Probability Ques)

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Can P[A | ( A intersection B )] be written as:
P(A intersection B )/ P(A intersection B )?

Given that A, B, and C are three sets where,
P( B )>0, P(A')>0, and P(A intersection B )>0.

By Conditional probablity laws:
P( A|B ) = P( A intersection B )/ P( B )

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