For the events $A$ and $B$ are such that $\mathrm{P}\left( A|B \right)=\frac{7}{10}$, \(\

Question

For the events $A$ and $B$ are such that $\mathrm{P}\left( A|B \right)=\frac{7}{10}$, $\mathrm{P}\left( B|A \right)=\frac{4}{15}$ and $\mathrm{P}\left( A\cup B \right)=\frac{3}{5}$. Find the exact values of $\mathrm{P}\left( A\cap B \right)$ ,[2] $\mathrm{P}\left( A'\cap B \right)$,[2] For a third event $C$, it is given that $P\left( C \right)=\frac{3}{10}$ and that $A$ and $C$ are independent. $\mathrm{P}\left( A'\cap C \right)$.[2] Hence state an inequality satisfied by $\mathrm{P}\left( A'\cap B\cap C \right)$.[1]

Accepted Answer

(i) ${\frac{28}{195}}$ (ii) ${\frac{4}{65}}$ (iii) ${\frac{9}{65}}$ (iv) ${0 \leq \mathrm{P}\left(A' \cap B \cap C\right) \leq \frac{9}{65}}$

2019 HCI P2 Q11

2019 HCI P2 Q11

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