For events $A$ and $B$, it is given that $\mathrm{P}\left( A\cap {B}' \right)=0.32$ and $\mathrm{P}\

Question

For events $A$ and $B$, it is given that $\mathrm{P}\left( A\cap {B}' \right)=0.32$ and $\mathrm{P}\left( B|A \right)=\frac{7}{23}$. Show that $\mathrm{P}\left( A\cap B \right)=0.14$. [2] Given further that $\mathrm{P}\left( A|B \right)=\frac{7}{19}$, find $\mathrm{P}\left( A\cup B \right)$. [2] It is given that $\mathrm{P}\left( C \right)=0.5$, where $C$ is an event such that events $A$ and $C$ are independent and $B$ and $C$ are independent. Find the greatest and least possible values of $P\left( {A}'\cap {B}'\cap {C}' \right)$. [4]

Accepted Answer

$0.08 \leq P(A' \cap B' \cap C) \leq 0.22$

2020 EJC P2 Q7

2020 EJC P2 Q7

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