2024 NYJC H1 Q8

Two events \(A\) and \(B\) are such that \(\mathrm{P}(A) = 3p\), \(\mathrm{P}(B) = p\), \(\mathrm{P}(A|B) = 0.4\) and \(\mathrm{P}(A \cup B) = 0.9\).

1. Find the value of \(p\).[3]
2. Explain what is meant by \(\mathrm{P}(A' \cap B')\) and find its value.[2]
3. Explain whether the events \(A\) and \(B\) are independent.[1]
4. Complete the Venn diagram to show the probability in each of the four regions.[1]