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 $$q-p$$.

×