Dominating Dice

Two players each roll a pair of standard 4-sided dice. The rolls for the first player are \(a_1, a_2\) with \(a_1 \leq a_2\) and the rolls for the second player are \(b_1,b_2\) with \(b_1 \leq b_2\). The probability that \(a_1 > b_1\) and \(a_2 > b_2\) can be expressed as \(\frac{a}{b}\) where \(a\) and \(b\) are coprime positive integers. What is the value of \(a + b\)?

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