Solution — 2016 Question 7 Probability

(a)

Venn diagram for 2016 Q7

(b)

(i)

\begin{matrix} P (A \cup B) & = P (A) + P (B) - P (A \cap B) \\ = 0.6 + 0.25 - 0.05 \\ = 0.8 ∎ \end{matrix}

(ii)

\begin{matrix} P (exactly one of A and B) & = P (A \cup B) - P (A \cap B) \\ = 0.8 - 0.05 \\ = 0.75 ∎ \end{matrix}

(c)

\begin{matrix} P (A | B^{'}) & = \frac{P (A \cap B^{'})}{P (B^{'})} \\ = \frac{0.55}{0.75} \\ = \frac{11}{15} ∎ \end{matrix}