Probability - Probability Bounds and Inequalities

For events \(A\) and \(B\), it is given that \(\mathrm{P}(A) = 0.6\), \(\mathrm{P}(A \cup B) = 0.7\) and \(\mathrm{P}(B \mid A) = 0.3\).

1. Show that \(\mathrm{P}(B) = 0.28\) and determine with a reason, if \(A\) and \(B\) are independent.[3]
2. An event \(C\) is such that \(A\) and \(C\) are mutually exclusive and \(\mathrm{P}(C) > 0.25\). Find the range of values of \(\mathrm{P}(B' \cap C)\).[3]