Question: Let \(A\), \(B\) , and \(C\) be three events with the following probabilities known.

\[\begin{array}{ll} P(A)=0.55 & P(A \cap B)=0.45 \\ P(B)=0.60 & P(A \cap C)=0.28 \\ P(C)=0.48 & P(B \cap C)=0.31 \end{array} \quad P(A \cap B \cap C)=0.20\]

1. Find \(P(B \cup C)\).
2. Find \(P\left((A \cup B)^{C}\right)\).
3. Find \(P(B \mid A)\).
4. Find \(P\left(A \mid C^{C}\right)\).

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