Question: 1. Let A and B be two events. Check if the following relations hold: (a) AUB=AU(ACB)? (b) B = (AnB) U(A'B) Please give your reasoning

1. Let A and B be two events. Check if the following relations hold: (a) AUB=AU(ACB)? (b) B = (AnB) U(A"'B) Please give your reasoning clearly. 2. Consider two events A and B such that P(A) = 1/3 and P(B) = 1/2. Determine the value of P(B H A\") for each of the following conditions: (a) A and B are disjoint; (b) A C B; (c) P(A n B) = g

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