Let the event of getting a greater number on the first die be G.
There are 5 ways to get a sum of 8 when two dice are rolled = {(2,6),(3,5),(4,4), (5,3),(6,2)}.
And there are two ways where the number on the first die is greater than the one on the second given that the sum should equal 8, G = {(5,3), (6,2)}.
Therefore, P(Sum equals 8) = 5/36 and P(G) = 2/36.
Now, P(G|sum equals 8)= P(G and sum equals 8)/P(sum equals 8)
= (2/36)/(5/36)
= 2/5