Solution — 2020 Question 9 Probability

(a)

$P (A | B^{'})$ is the probability that $A$ occurs given that $B$ did not occur $∎$

(b)

By the conditional probability formula,

\begin{matrix} P (A | B^{'}) & = \frac{P (A \cap B^{'})}{P (B^{'})} \\ 0.8 & = \frac{P (A \cap B^{'})}{1 - 0.7} \\ P (A \cap B^{'}) & = 0.24 ∎ \end{matrix}

(c)

We find the probability that at least one of $A$ and $B$ occurs, which is $P (A \cup B) .$

\begin{matrix} P (A \cup B) \\ = 0.7 + 0.24 \\ = 0.94 ∎ \end{matrix}

Use a Venn diagram to visualize this.

(d)

Venn diagram