2013 CJC P2 Q6

For events \(A\) and \(B\), it is given that \(\mathrm{P}\left( B \right)=\frac{3}{5}\), \(\mathrm{P}\left( A\cup B \right)=\frac{7}{8}\) and \(\mathrm{P}\ (A'\cap B)=\frac{11}{36}\).

Find

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

A third event \(C\), has \(\mathrm{P}\ \left( C \right)=\frac{4}{7}\) and that \(A\) and \(C\) are independent

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