2025 TGM P2 Q7

Two independent events \(A\) and \(B\) are such that \(A\) is a subset of \(B\).

1. State the condition(s) that events \(A\) and \(B\) must satisfy.[2]

You are now given that \(A\) is not a subset of \(B\), \(\mathrm{P}(A' \cup B) = \frac{3}{5}\) and \(\mathrm{P}(B) = \frac{1}{3}\).
Find

2. \(\mathrm{P}(A)\).[3]

For a third event \(C\), where \(\mathrm{P}(C) = \frac{1}{4}\) and \(\mathrm{P}(A \cap C) = \frac{1}{8}\).
Find

3. \(\mathrm{P}(A' \cap C)\),[1]
4. exactly the maximum and minimum possible values of \(\mathrm{P}(A' \cap B' \cap C)\).[2]