Question

Nonstandard dice can produce interesting distributions of outcomes. you have two balanced, six-sided dice. one is a standard die, with faces having 1, 2, 3, 4, 5, and 6 spots. the other die has three faces with 0 spots and three faces with 6 spots. what are the possible values for the total number of spots y on the up-faces when you roll these two dice?

Answer 1

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
   
One die can show the values 1-6, while the other die can only show 0 or 6. So the possible totals are 1 through 6 plus 0 and 1 through 6 plus 6. Written out, one-by-one, this gives: 1+0 = 1 2+0 = 2 3+0 = 3 4+0 = 4 5+0 = 5 6+0 = 6 1+6 = 7 2+6 = 8 3+6 = 9 4+6 = 10 5+6 = 11 6+6 = 12