For events $A$ and $B$, it is given that $\mathrm{P}\left( B' \right)=0.51$, \(\mathrm{P}

Question

For events $A$ and $B$, it is given that $\mathrm{P}\left( B' \right)=0.51$, $\mathrm{P}\left( A'\cap B' \right)=0.15$. Find $\mathrm{P}\left( A\cap B' \right)$.[2] It is also given that $\mathrm{P}\left( B\left| \,A \right. \right)=\frac{11}{29}$. Find $\mathrm{P}\left( A \right)$.[3] For a third event $C$, it is given that $A$ and $C$ are independent of each other, and $B$ and $C$ are mutually exclusive. Find the maximum value of $\mathrm{P}\left( C \right)$.[3]

Accepted Answer

(a) $0.36$ (b) $0.58$ (c) $\dfrac5{14}$

2023 TMJC P2 Q5

2023 TMJC P2 Q5

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