Events $A$ and $B$ are such that $P(A | B) = \frac{7}{10}$, $P(B) = \frac{1}{3}$ and \(

Question

Events $A$ and $B$ are such that $P(A | B) = \frac{7}{10}$, $P(B) = \frac{1}{3}$ and $P(A \cup B) = \frac{3}{5}$. Find $P(A \cap B)$. Hence show that $P(A) = \frac{1}{2}$.[4] Find the probability that exactly one of $A$ and $B$ occurs.[2] Determine whether the events $A$ and $B$ are independent.[1]

Accepted Answer

(a)$\frac{1}{2}$ (b)$\frac{11 }{30}$

2024 ACJC P1 Q8

2024 ACJC P1 Q8