The events $A$ and $B$ are such that $\mathrm{P}(B) = \frac{1}{3}$, \(\mathrm{P}(A|B) = \

Question

The events $A$ and $B$ are such that $\mathrm{P}(B) = \frac{1}{3}$, $\mathrm{P}(A|B) = \frac{2}{5}$ and $\mathrm{P}(A \cup B) = \frac{3}{5}$. Find $\mathrm{P}(A)$ and hence, determine whether events $A$ and $B$ are independent.[4] Find the exact value of $\mathrm{P}(A' \cap B)$.[1] For a third event $C$, it is given that $\mathrm{P}(C) = \frac{1}{2}$ and that $A$ and $C$ are mutually exclusive. Find exactly the greatest and least possible values of $\mathrm{P}(B' \cap C)$.[4]

Accepted Answer

(a) $\mathrm P(A)=\dfrac25$, and $A$ and $B$ are independent (b) $\mathrm P(A'\cap B)=\dfrac15$ (c) Least $\dfrac3{10}$, greatest $\dfrac25$

2025 JPJC P2 Q9

2025 JPJC P2 Q9

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