For events $A$ and $B$, it is given that $P\left( A \right)=\frac{1}{8}$, \(P\left( A\cup

Question

For events $A$ and $B$, it is given that $P\left( A \right)=\frac{1}{8}$, $P\left( A\cup B \right)=\frac{9}{16}$ and $P\left( A\cap {B}' \right)=\frac{1}{16}$. Find $P\left( B \right)$.[1] Determine, with a reason, whether the events $A$ and $B$ are independent.[2] For a third event $C$, it is given that $P\left( C \right)=\frac{3}{8}$, $P\left( A\cap B\cap C \right)=\frac{1}{64}$ and $C$ is independent of $A$. Find $P\left( {A}'\cap C \right)$.[1] Find the range of values for $P\left( A'\cap {B}'\cap {C}' \right)$.[3]

Accepted Answer

(i) ${\frac{1}{2}}$ (ii) Since ${\mathrm{P}(A)\mathrm{P}(B) = \mathrm{P}(A \cap B) = \frac{1}{16}}$, the events ${A}$ and ${B}$ are independent. (iii) ${\frac{21}{64}}$ (iv) ${\frac{7}{64} \leq P(A' \cap B' \cap C') \leq \frac{7}{16}}$

2024 TMJC P2 Q5

2024 TMJC P2 Q5

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