2025 ACJC P2 Q6

If \(\mathrm{P}(B|A) = 0.2\), \(\mathrm{P}(A|B) = 0.6\) and \(\mathrm{P}(A' \cap B') = 0.3\), find \(\mathrm{P}(A \cap B)\).[3]

The events \(X\), \(Y\) and \(Z\) are such that the events \(X\) and \(Z\) are mutually exclusive. Given further that \(\mathrm{P}(X \cap Y) = 0.1\), \(\mathrm{P}(X' \cap Y) = 0.35\), \(\mathrm{P}(Y \cap Z) = 0.2\), and \(\mathrm{P}(X \cup Y \cup Z) = 0.95\), find the minimum and maximum values of \(\mathrm{P}(X)\).[3]