For events $A$ and $B$, it is given that $\mathrm{P}\left( A \right)=\frac{11}{20}$, $\mathrm{P}\lef

Question

For events $A$ and $B$, it is given that $\mathrm{P}\left( A \right)=\frac{11}{20}$, $\mathrm{P}\left( B \right)=\frac{2}{5}$ and $\mathrm{P}\left( A\cap B \right)=\frac{1}{4}$. Find the probability where event $A$ occurs or event $B$ occurs but not both. [1] Find the probability where event $B$ has occurred but not $A$. [1] Find a third event $C$, it is given that $\mathrm{P}\left( C \right)=\frac{1}{2}$ and that $A$ and $C$ are independent. Find the range of values of $\mathrm{P}\left( A'\cap B'\cap C \right)$. [3]

Accepted Answer

(i) $\frac{9}{20}$ (ii) $\frac{3}{20}$ (iii) $\frac{3}{40}\le \mathrm{P}\left( A'\cap B'\cap C \right)\le \frac{3}{10}$

2018 SRJC P2 Q10(b)

2018 SRJC P2 Q10(b)

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