N2015 P2 Q9

For events \(A\), \(B\) and \(C\) it is given that \(\mathrm{P}\left( A \right)=0.45\), \(\mathrm{P}\left( B \right)=0.4\), \(\mathrm{P}\left( C \right)=0.3\) and \(P\left( A\cap B\cap C \right)=0.1\). It is also given that events \(A\) and \(B\) are independent, and that events \(A\) and \(C\) are independent.

1. Find \(\mathrm{P}\left( B|A \right)\).[1]
2. Given also that event \(B\) and \(C\) are independent, find \(\mathrm{P}\left( A'\cap B'\cap C' \right)\).[3]
3. Given instead that events \(B\) and \(C\) are not independent, find the greatest and least possible values of \(\mathrm{P}\left( A'\cap B'\cap C' \right)\).[4]