# A discrete mathematics problem by Josh Rowley

$$a$$ and $$b$$ are 2 real numbers randomly chosen from the interval $$[0,4]$$. Given that $$a+b \geq 1$$, the probability that $$|a-b| \le 1$$ can be expressed in the form $$\dfrac{p}{q}$$ where $$p$$ and $$q$$ are coprime positive integers. What is $$p+q$$?

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