1 For the events \(A\) and \(B , \mathrm { P } ( A ) = 0.3 , \mathrm { P } ( B ) = 0.6\) and \(\mathrm { P } \left( A ^ { \prime } \cap B ^ { \prime } \right) = c\), where \(c \neq 0\).
- Find \(\mathrm { P } ( A \cap B )\) in terms of \(c\).
- Find \(\mathrm { P } ( B \mid A )\) and deduce that \(0.1 \leqslant c \leqslant 0.4\).