For events $A$, $B$ and $C$, it is given that $\mathrm{P}\left( A \right)=0.4$, \(\math

Question

For events $A$, $B$ and $C$, it is given that $\mathrm{P}\left( A \right)=0.4$, $\mathrm{P}\left( C \right)=0.3$ and $\mathrm{P}\left( B\cap C \right)=0.1$. It is also given that events $A$ and $B$ are mutually exclusive, and that events $A$ and $C$ are independent. Find $\mathrm{P}\left( A\cap B \right)$.[1] Find $\mathrm{P}\left( \left. A \right|C \right)$.[1] Given also that events $B$ 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 $\mathrm{P}\left( B \right)$.[2]

Accepted Answer

(i) ${\mathrm{P}(A \cap B) = 0}$ (ii) ${\mathrm{P}(A) = 0.4}$ (iii) ${\mathrm{P}(A' \cap B' \cap C') = 0.187}$ (3 s.f.) (iv) Least ${\mathrm{P}(B) = 0.1}$, greatest ${\mathrm{P}(B) = 0.52}$

2023 MI P2 Q8

2023 MI P2 Q8

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