A discrete mathematics problem by Shanthanu Rai

In a bag there are 15 balls of either red or green color. Let \(G_k\) be the event that it contains exactly \(k\) green balls and its probability is proportional to \(k^2\). Now a ball is chosen at random. Let \(P(A)\) be the probability that the ball is red. If \(P(A)=\dfrac{p}{q}\), where \(p\) and \(q\) are coprime positive integers, find \(q-p\).

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