2024 EJC H1 Q7

\(A\) and \(B\) are events such that \(\mathrm{P}(A) = p\), \(\mathrm{P}(B) = 3p\) and \(\mathrm{P}(A' \cap B') = 0.08\).

1. Find an expression for \(\mathrm{P}(A \cap B)\) in terms of \(p\).[2]

It is also given that \(\mathrm{P}(A \cap B) = 2\mathrm{P}(A \cap B')\).

2. Show that \(p = 0.276\).[3]
3. Explain what is meant by \(\mathrm{P}(B | A)\) and find its value.[2]