For events $A$ and $B$, it is given that $\mathrm{P}\left( B \right)=\frac{7}{27}$, \(\ma

Question

For events $A$ and $B$, it is given that $\mathrm{P}\left( B \right)=\frac{7}{27}$, $\mathrm{P}\left( B|A \right)=\frac{2}{9}$ and $\mathrm{P}\left( A|B' \right)=\frac{7}{10}$. State, with reason, whether $A$ and $B$are independent.[1] Find $\mathrm{P}\left( A\cup B \right)$.[3] Find $\mathrm{P}\left( A\cap B \right)$.[3] For a third event $C$, it is given that $\mathrm{P}\left( B\cap C \right)=\frac{1}{18}$ and that $A$ and $C$ are mutually exclusive. Find the range of $\mathrm{P}\left( C \right)$.[2]

Accepted Answer

(i) Not independent (ii) $\frac79$ (iii) $\frac4{27}$ (iv) $\frac1{18}\leq P(C)\leq\frac5{18}$

2015 PJC P2 Q11

2015 PJC P2 Q11

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