For events $\mathrm{A}$ and $\mathrm{B}$, it is given that $\mathrm{P}(A)=0.7$, \(\mathrm{P}(B

Question

For events $\mathrm{A}$ and $\mathrm{B}$, it is given that $\mathrm{P}(A)=0.7$, $\mathrm{P}(B)=0.6$ and $\mathrm{P}(A\left| B' \right.)=0.8$. Find $\mathrm{P}(A\cap B')$,[2] $\mathrm{P}(A\cup B)$,[2] $\mathrm{P}(B'\left| A \right.)$,[2] Find a third event $C$, it is given that $\mathrm{P}(C)=0.5$ and that $A$ and $C$ are independent. Find $\mathrm{P}\left( A'\cap C \right)$[2] Hence state an inequality satisfied by $\mathrm{P}(A'\cap B\cap C)$.[1]

Accepted Answer

(i) $0.32$ (ii) $0.92$ (iii) $\frac{16}{35}$ (iv) $0.15$ (v) $0.07 \leq \mathrm{P}(A^{\prime} \cap B \cap C) \leq 0.15$

N2010 P2 Q7

N2010 P2 Q7

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