(a)     Find the percentage of the population that has been vaccinated.

(b)     A randomly chosen person catches the virus. Find the probability that this person has been vaccinated.

(a)

using the law of total probabilities:     (M1)

\(0.1p + 0.3\left( {1 - p} \right) = 0.22\)     A1

\(0.1p + 0.3 - 0.3p = 0.22\)

\(0.2p = 0.88\)

\(p = \frac{{0.88}}{{0.2}} = 0.4\)

\(p = 40\% \) (accept \(0.4\))     A1

(b)     required probability \( = \frac{{0.4 \times 0.1}}{{0.22}}\)     M1

\( = \frac{2}{{11}}\)   (\(0.182\))     A1

[5 marks]

Most candidates who successfully answered this question had first drawn a tree diagram, using a symbol to denote the probability that a randomly chosen person had received the influenza virus. For those who did not draw a tree diagram, there was poor understanding of how to apply the conditional probability formula.