Solution — 2019 Question 8 Probability

(a)

By the conditional probability formula,

$\begin{matrix} P (A | B) & = \frac{P (A \cap B)}{P (B)} \\ 0.1 & = \frac{P (A \cap B)}{0.4} \\ P (A \cap B) & = 0.04 ∎ \end{matrix}$

(b)

$P (A^{'} \cap B)$ is the probability that event $B$ occurs and event $A$ does not occur $∎$

(c)

Using $P (A) = 0.6$ and $P (A \cap B) = 0.04,$

Venn diagram

$\begin{matrix} P (A^{'} \cup B) \\ = 1 - 0.56 \\ = 0.44 ∎ \end{matrix}$