2018 SRJC P2 Q10(b)

For events \(A\) and \(B\), it is given that \(\mathrm{P}\left( A \right)=\frac{11}{20}\), \(\mathrm{P}\left( B \right)=\frac{2}{5}\) and \(\mathrm{P}\left( A\cap B \right)=\frac{1}{4}\).

1. Find the probability where event \(A\) occurs or event \(B\) occurs but not both.[1]
2. Find the probability where event \(B\) has occurred but not \(A\).[1]

Find a third event \(C\), it is given that \(\mathrm{P}\left( C \right)=\frac{1}{2}\) and that \(A\) and \(C\) are independent.

3. Find the range of values of \(\mathrm{P}\left( A'\cap B'\cap C \right)\).[3]