2024 JPJC H1 Q7

\(A\) and \(B\) are events such that

\[\mathrm{P}(B)=x, \quad \mathrm{P}(A' \cap B')=\frac{3}{20} \quad \text{and} \quad \mathrm{P}(A|B)=\frac{1}{4}\]

1. Find an expression for \(\mathrm{P}(A)\) in terms of \(x\).[3]

It is also given that \(\mathrm{P}(A \cap B')=\frac{5}{3}\mathrm{P}(A \cap B)\).

2. Find the value of \(x\).[3]
3. Find \(\mathrm{P}(B'|A')\).[2]