2/n where n is the number of faces on the die
A 6-sided die could be numbered 1, 2, 2, 3, 4, 4 to meet the probability requirements 2/6 = 1/3 of the faces have the number 2, so the probability of 2 would be 1/3.
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To meet the probability requirements nicely requires a die with a number of faces that is a multiple of 3. The regular solids meeting this requirement are
A dodecahedron could be numbered 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4 and the probability of a 2 would be the same as for a cube. It could more reasonably be numbered 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, in which case, the probability of 2 would be 1/6.
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If you use some other shape or put blank faces on the die (say a 20-faced die with 2 blanks), then the probability will be different from the numbers above. If you still use 2 faces for each even number, then the probability of 2 using an n-faced die is 2/n.
