Question: Let A and B be two events in a sample space with P(A) = ???? and P(B) = ????. Confirm the validity for each

Let A and B be two events in a sample space Ω with P(A) = ???? and P(B) = ????. Confirm the validity for each of the following:

(i) P(A′B′) = 1 − ???? − ???? + P(AB);

(ii) ???? + ???? − 1 ≤ P(AB) ≤ min{????, ????};

(iii) max{????, ????} ≤ P(A ∪ B) ≤ ???? + ????.

Suppose P(A) = 0.75 and P(B) = 0.80.What is the range of possible values for each of P(A ∪ B) and P(AB)?

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