Two events $$\(A\)$$ and $$\(B\)$$ are such that $$\(\mathrm{n}(A)=62 \mathrm{n}(B)=30\)$$ and $$\(\mathrm{n}(A \cup B)=68\)$$ Given that $$\(\mathrm{n}(\mathscr{E})=80\)$$ (a) complete the Venn diagram to show the number of elements in each region. (2) An element is chosen at random from $$\(\mathscr{E}\)$$. (b) Using the Venn diagram, find the probability that this element is in (i) $$\(A \cap B\)$$ (1) (ii) $$\(A \cup B^{\prime}\)$$ (2)

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