2024 DHS H1 Q7

It is given that for two events \(A\) and \(B\),

\[\mathrm{P}(A) = 0.35, \mathrm{P}(B) = x \text{ and}\hspace{0.5em} \mathrm{P}(A' \cap B') = 0.25.\]

1. Find \(\mathrm{P}(A \cup B)\).[1]
2. Given that \(A\) and \(B\) are independent, find the value of \(x\).[3]

The event \(C\) is such that \(\mathrm{P}(A | C) = 0.35\).

3. It is given that \(\mathrm{P}(A \cap C') = 0.15\). Find \(\mathrm{P}(C)\).[3]
4. Complete the Venn diagram to show the probability in each of the four regions.[1]