A roll of three dice

Discrete Mathematics Level pending

Arjuna is going to roll three fair ten-sided dice with faces labelled \(0, 1, 2, \ldots , 9\).

First he rolls two dice, and finds the sum of the two rolls.
Then he rolls the third die.

If the probability that the sum of the first two rolls equals the third roll can be expressed as \(\frac ab\), where \(a,b\) are coprime positive integers, then what is \(a + b\)?

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