Let (A) and (B) be disjoint events with (P(A)=0.3) and (P(B)=0.45). Determine the probabilities (P(A cup B),

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Let \(A\) and \(B\) be disjoint events with \(P(A)=0.3\) and \(P(B)=0.45\). Determine the probabilities \(P(A \cup B), P(\overline{A \cup B}), P(\bar{A} \cup \bar{B})\), and \(P(\bar{A} \cap B)\).

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