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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