Roll the dice thrice 3

A fair dice is numbered with \( 1,-2,0,-1,3,2\) on its faces.

The probability of getting a sum of 4 after rolling the dice thrice can be expressed as \(\frac{a}{b}\) where \(a,b\) are relatively prime.

Find \(a+b\) .

Try these too: Part I, Part II.
Image Credit: Flickr Gard Rimestad.

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