The Venn diagram shows the events $$\(A, B\)$$ and $$\(C\)$$ and their associated probabilities, where $$\(p\)$$ and $$\(q\)$$ are probabilities. (a) Find $$\(\mathrm{P}(B)\)$$ (1) (b) Determine whether or not $$\(A\)$$ and $$\(B\)$$ are independent. (2) Given that $$\(\mathrm{P}(C \mid B)=\mathrm{P}(C)\)$$ (c) find the value of $$\(p\)$$ and the value of $$\(q\)$$ (3) The event $$\(D\)$$ is such that - $$\(A\)$$ and $$\(D\)$$ are mutually exclusive - $$\(\mathrm{P}(B \cap D)> 0\)$$ (d) On the Venn diagram show a possible position for the event $$\(D\)$$ (1)

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