Let A and B be two disjoint events of the same sample space with P(A) 0 and P(B) 0. Show that P(A|A UB)

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Let A and B be two disjoint events of the same sample space with P(A) ≠ 0 and P(B) ≠ 0. Show that

P(A|A UB) P(B|AUB) 1 P(A) P(B) P(A) + P(B)