It is given that for two events $A$ and $B$, \[\mathrm{P}(A) = 0.35, \mathrm{P}(B) = x \text{ an

Question

It is given that for two events $A$ and $B$, $$\mathrm{P}(A) = 0.35, \mathrm{P}(B) = x \text{ and}\hspace{0.5em} \mathrm{P}(A' \cap B') = 0.25.$$ Find $\mathrm{P}(A \cup B)$.[1] Given that $A$ and $B$ are independent, find the value of $x$.[3] The event $C$ is such that $\mathrm{P}(A | C) = 0.35$. It is given that $\mathrm{P}(A \cap C') = 0.15$. Find $\mathrm{P}(C)$.[3] Complete the Venn diagram to show the probability in each of the four regions.[1]

Accepted Answer

(a)0.75 (b)0.615 (c)$\frac{4}{7}$

2024 DHS H1 Q7

2024 DHS H1 Q7