$A$ and $B$ are independent events such that $\mathrm{P}\left( \left. A \right|B \right)=\frac{1}{5}

Question

$A$ and $B$ are independent events such that $\mathrm{P}\left( \left. A \right|B \right)=\frac{1}{5}$and $\mathrm{P}\left( A\cup B \right)=\frac{2}{3}$. Find the exact value of $\mathrm{P}\left( A\cap B' \right)$. [4] For a third event $C$ , it is given that $\mathrm{P}\left( C \right)=\frac{2}{7}$ and that $A$ and $C$ are mutually exclusive. Find the range of values of $\mathrm{P}\left( B'\cap C' \right)$. [3]

Accepted Answer

$\dfrac{11}{84} \leq P(B' \cap C') \leq \dfrac{5}{12}$

2021 TMJC P2 Q7

2021 TMJC P2 Q7

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