The answer posted above is correct. However the same answer can be arrived at in another way also.
Tho get a total of 8 for 2 dies none of the dice must have a '1'.
The probability that the first dice will not have a '1', or that it will have 2, 3, 4, 5, or 6, are:
Probability of first dice not getting 1 = 5/6
This is because the probability of getting any number from 1 to 6 are equal.
For each occurrence of the number 2 to 6 for dice the second dice must get a number given by:
Required number if dice 2 = 8 - n
Where:
n = number of dice 1
As the probability of getting any one number is equal to 1/6, the probability that the second dice will have exactly the required number is:
Probability of second dice getting the number (8 - n) = 1/6
The probability of getting sum of 8:
Probability that sum is 8 =
(Probability of first dice not getting 1)*(Probability of second dice getting the number (8 - n))
= (5/6)*(1/6) = 5/36
Answer:
Probability of sum of two dice as 8 = 5/36