Dominating Dice

Probability Level 5

Two players each roll a pair of standard 4-sided dice. The rolls for the first player are a1,a2a_1, a_2 with a1a2a_1 \leq a_2 and the rolls for the second player are b1,b2b_1,b_2 with b1b2b_1 \leq b_2. The probability that a1>b1a_1 > b_1 and a2>b2a_2 > b_2 can be expressed as ab\frac{a}{b} where aa and bb are coprime positive integers. What is the value of a+ba + b?

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