For events $A$ and $B$, it is given that $\mathrm{P}\left( A \right)=\frac{3}{4}$, \(\mat

Question

For events $A$ and $B$, it is given that $\mathrm{P}\left( A \right)=\frac{3}{4}$, $\mathrm{P}\left( A'|B \right)=\frac{1}{2}$ and $\mathrm{P}\left( A\cup B \right)=\frac{19}{20}$. Find $\mathrm{P}\left( A\cap B \right)$,[3] $\mathrm{P}\left( A'\cup B' \right)$,[2] $\mathrm{P}\left( B|A' \right)$.[2] For a third event $C$, it is given that $\mathrm{P}\left( C \right)=\frac{1}{2}$ and that $A$ and $C$ are independent. Find $\mathrm{P}\left( A'\cap C \right)$.[2] Hence state an inequality satisfied by $\mathrm{P}\left( A'\cap B\cap C \right)$.[1]

Accepted Answer

(i) ${\frac{1}{5}}$ (ii) ${\frac{4}{5}}$ (iii) ${\frac{4}{5}}$ (iv) ${0.125}$ (v) ${\mathrm{P}(A' \cap B \cap C) \leq 0.125}$

2018 TPJC MYE P2 Q7

2018 TPJC MYE P2 Q7

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