For events $A$, $B$ and $C$ it is given that $\mathrm{P}\left( A \right)=0.45$, $\mathrm{P}\left( B

Question

For events $A$, $B$ and $C$ it is given that $\mathrm{P}\left( A \right)=0.45$, $\mathrm{P}\left( B \right)=0.4$, $\mathrm{P}\left( C \right)=0.3$ and $P\left( A\cap B\cap C \right)=0.1$. It is also given that events $A$ and $B$ are independent, and that events $A$ and $C$ are independent. Find $\mathrm{P}\left( B|A \right)$. [1] Given also that event $B$ and $C$ are independent, find $\mathrm{P}\left( A'\cap B'\cap C' \right)$. [3] Given instead that events $B$ and $C$ are not independent, find the greatest and least possible values of $\mathrm{P}\left( A'\cap B'\cap C' \right)$. [4]

Accepted Answer

(i) 0.4; (ii) 0.185; (iii) greatest = 0.33, least = 0.165

N2015 P2 Q9

N2015 P2 Q9

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