The events $A$, $B$ and $C$ are such that $\mathrm{P}\left( A \right)=0.1$, \(\mathrm{P

Question

The events $A$, $B$ and $C$ are such that $\mathrm{P}\left( A \right)=0.1$, $\mathrm{P}\left( B \right)=0.2$ and $\mathrm{P}\left( C \right)=c$. $A$ and $B$ are independent events. $A$ and $C$ are mutually exclusive events. State the values of $\mathrm{P}\left( \left. A \right|B \right)$ and $\mathrm{P}\left( \left. A \right|C \right)$.[2] It is given that $\mathrm{P}\left( A\cup B \right)=\mathrm{P}\left( A'\cap C' \right)$. Find the value of $c$.[3] Find the maximum and minimum possible values of $\mathrm{P}\left( A'\cap B'\cap C' \right)$.[4]

Accepted Answer

(a) $P(A\mid B)=0.1$, $P(A\mid C)=0$ (b) $c=0.62$ (c) minimum $0.10$, maximum $0.28$

2023 NJC P2 Q8

2023 NJC P2 Q8

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