Let B be an event of a sample space S with P (B) > 0. For

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QUESTION:

Let B be an event of a sample space S with P (B) > 0. For a subset A of S, define Q(A) = P (A | B). By Theorem 3.1 we know that Q is a probability function. For E and F, events of S 4 P (FB) > 0 5 , show that Q(E | F ) = P (E | FB).

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QUESTION:

Let B be an event of a sample space S with P (B) > 0. For a subset A of S, define Q(A) = P (A | B). By Theorem 3.1 we know that Q is a probability function. For E and F, events of S 4 P (FB) > 0 5 , show that Q(E | F ) = P (E | FB).

ANSWER:

Step 1 of 2

Let be an event of a sample space with . For a subset of , a probability function is defined by .

Let and be any events of with .

To prove that

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