The Venn diagram shows the events $$\(A, B, C\)$$ and $$\(D\)$$, where $$\(p, q, r\)$$ and $$\(s\)$$ are probabilities. (a) Write down the value of (i) $$\(\mathrm{P}(A)\)$$ (ii) $$\(\mathrm{P}(A \mid B)\)$$ (iii) $$\(\mathrm{P}(A \mid C)\)$$ (3) Given that $$\(\mathrm{P}\left(B^{\prime} \cap D^{\prime}\right)=\frac{7}{10}\)$$ and $$\(\mathrm{P}(C \mid D)=\frac{3}{5}\)$$ (b) find the exact value of $$\(q\)$$ and the exact value of $$\(r\)$$ (6) Given also that $$\(\mathrm{P}\left(B \cup C^{\prime}\right)=\frac{5}{8}\)$$ (c) find the exact value of $$\(s\)$$ (2)

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