A bag contains a large number of counters with one of the numbers 5,10 or 20 written on each of them in the ratio $$\(5: 2: a\)$$ A jar contains a large number of counters with one of the numbers 5 or 10 written on each of them in the ratio $$\(1: 3\)$$ One counter is selected at random from the bag and then two counters are selected at random from the jar. The random variable $$\(R\)$$ represents the range of the numbers on the 3 counters. Given that $$\(\mathrm{P}(R=15)=\frac{63}{256}\)$$ (a) by forming and solving an equation in $$\(a\)$$, show that $$\(a=9\)$$ (3) (b) find the sampling distribution of $$\(R\)$$ (6)

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