For events $A$ and $B$, it is given that $\mathrm{P}\left( A'\cup B' \right)=0.82$ and \(

Question

For events $A$ and $B$, it is given that $\mathrm{P}\left( A'\cup B' \right)=0.82$ and $\mathrm{P}\left( A|B \right)=0.4$. Find $\mathrm{P}\left( B \right)$.[2] Hence find an inequality for $\mathrm{P}\left( A\cap B' \right)$.[2] A third event $C$ is such that $\mathrm{P}\left( C \right)=0.1$. $A$ and $C$ are mutually exclusive. $B$ and $C$ are independent. Find $\mathrm{P}\left( A'\cap B\cap C' \right)$.[3]

Accepted Answer

(a) ${0.45}$ (b) ${\mathrm{P}\left(A \cap B'\right) \leq 0.55}$ (c) ${0.225}$

2023 YIJC P2 Q6

2023 YIJC P2 Q6

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