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That's a very nice problem !

Total number of possible outcomes with two dice = 36.

Factors of twelve = 1, 2, 3, 4, 6, and 12.

Number of ways to roll a '1' = zero

Number of ways to roll a 2 = 1 . .. . (snake-eyes)

Number of ways to roll 3 = 2 . . . . . (1,2 and 2,1)

Number of ways to roll 4 = 3 . . . . . (1,3 / 2,2 and 3/1)

Number of ways to roll 6 = 5 . . . . . (1,5 / 2,4 / 3,3 / 4,2 and 5,1)

Number of ways to roll 12 = 1 . . . . (box-cars)

Total number of successful rolls = 12

Probability = 12/36 = 1/3 = 33 and 1/3 percent.

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Q: When rolling two dice what is the probability of the sum being a factor of twelve?
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