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

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47. 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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