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Show that the postulates of probability are satisfied by conditional

Show that the postulates of probability are satisfied by conditional probabilities. In other words, show that if P(B) ≠ 0, then

(a) P(A| B) ≥ 0;

(b) P(B| B) = 1;

(c) P(A1 ∪ A2 .. ∪ . | B) = P(A1| B) + P(A2| B) + · · · for Any sequence of mutually exclusive events A1, A2, ∪ . ..

(a) P(A| B) ≥ 0;

(b) P(B| B) = 1;

(c) P(A1 ∪ A2 .. ∪ . | B) = P(A1| B) + P(A2| B) + · · · for Any sequence of mutually exclusive events A1, A2, ∪ . ..

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