3 For events \(A , B\) and \(C\) it is given that \(\mathrm { P } ( A ) = 0.6 , \mathrm { P } ( B ) = 0.5 , \mathrm { P } ( C ) = 0.4\) and \(\mathrm { P } ( A \cap B \cap C ) = 0.1\). It is also given that events \(A\) and \(B\) are independent and that events \(A\) and \(C\) are independent.

1. Find \(\mathrm { P } ( B \mid A )\).
2. Given also that events \(B\) and \(C\) are independent, find \(\mathrm { P } \left( A ^ { \prime } \cap B ^ { \prime } \cap C ^ { \prime } \right)\).
3. Given instead that events \(B\) and \(C\) are not independent, find the greatest and least possible values of \(\mathrm { P } \left( A ^ { \prime } \cap B ^ { \prime } \cap C ^ { \prime } \right)\).