Find \({\text{P}}(B)\).

Find \({\text{P}}(A \cup B)\).

valid interpretation (may be seen on a Venn diagram)     (M1)

eg\(\,\,\,\,\,\)\({\text{P}}(A \cap B) + {\text{P}}(A' \cap B),{\text{ }}0.2 + 0.6\)

\({\text{P}}(B) = 0.8\)     A1     N2

[2 marks]

valid attempt to find \({\text{P}}(A)\)     (M1)

eg\(\,\,\,\,\,\)\({\text{P}}(A \cap B) = {\text{P}}(A) \times {\text{P}}(B),{\text{ }}0.8 \times A = 0.2\)

correct working for \({\text{P}}(A)\)     (A1)

eg\(\,\,\,\,\,\)\(0.25,{\text{ }}\frac{{0.2}}{{0.8}}\)

correct working for \({\text{P}}(A \cup B)\)     (A1)

eg\(\,\,\,\,\,\)\(0.25 + 0.8 - 0.2,{\text{ }}0.6 + 0.2 + 0.05\)

\({\text{P}}(A \cup B) = 0.85\)     A1     N3

[4 marks]