For a fixed event B, show that the collection P(A|B), defined for all events A, satisfies the

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For a fixed event B, show that the collection P(A|B), defined for all events A, satisfies the three conditions for a probability. Conclude from this that P(A|B) = P(A|BC)P (C|B) + P(A|BCc)P (Cc|B)

Then directly verify the preceding equation.

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