First we need to find a list of what numbers from both sets {1,2,3,4,5,6,7,8,9,10,11,12} and {1,2,3,4,5,6,7,8,9,10,11,12} will add up to 19 or greater. These are:

12+7=19

12+8=20

12+9=21

12+10=22

12+11=23

12+12=24

11+8=19

11+9=20

11+10=21

11+11=22

10+9=19

10+10=20

This amounts to 12 combinations. Since this can happen on opposite dice, we multiply by 2 to get 24 outcomes. The total number of outcomes are 12*12=144. So, the answer is 24/144 = **1/6**.

Let me know if I did anything wrong!