Let the dice be red and green.
There are a total of #6 xx 6 = 36# possible outcomes.
Whatever number appears on the red die, the number on the green die can cause the total to be #7#. So there are #6# ways to get a total of #7#.
Of the remaining #36 - 6 = 30# outcomes, half (#15#) produce a total score greater than #7# and half (#15#) produce a total score less than #7#. To see this, consider what happens if you roll the dice, note down the score then turn the dice completely over. The sum of the new score and old score will be #14#, since the oppositie sides of a die add up to #7#. So for each outcome producing a total less than #7# there's an outcome producing a total more than #7# and vice versa.
So there are #15# outcomes out of a possible #36# which produce a total of at least #8#.
Therefore the probability of rolling such an outcome is:
#15/36 = (3*5)/(3*12) = 5/12#
