There are 20 counters in bag $$\(\mathbf{X}\)$$. 7 of the counters are green. 10 of the counters are red. The rest of the counters are blue. Ruth puts the counter back into bag $$\(\mathbf{X}\)$$. Bag $$\(\mathbf{Y}\)$$ only contains green counters, red counters and blue counters. In bag $$\(\mathbf{Y}\)$$ there are, 2 more green counters than in bag $$\(\mathbf{X}\)$$ 1 more red counter than in bag $$\(\mathbf{X}\)$$ 2 more blue counters than in bag $$\(\mathbf{X}\)$$ Adam takes at random a counter from bag $$\(\mathbf{Y}\)$$. Ruth takes at random a counter from bag $$\(\mathbf{X}\)$$. (c) Who has the greater probability of taking a green counter, Adam or Ruth? Show your working clearly. (3)

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