2023 TMJC P2 Q5

For events \(A\) and \(B\), it is given that \(\mathrm{P}\left( B' \right)=0.51\), \(\mathrm{P}\left( A'\cap B' \right)=0.15\).

1. Find \(\mathrm{P}\left( A\cap B' \right)\).[2]

It is also given that \(\mathrm{P}\left( B\left| \,A \right. \right)=\frac{11}{29}\).

2. Find \(\mathrm{P}\left( A \right)\).[3]

For a third event \(C\), it is given that \(A\) and \(C\) are independent of each other, and \(B\) and \(C\) are mutually exclusive.

3. Find the maximum value of \(\mathrm{P}\left( C \right)\).[3]