Each die has 6 faces with numbers from 1 to 6. When 2 dice are thrown the sum of the numbers that show up can be 2, 3, 4, 5, 6,7 8, 9, 10, 11, 12.
There can be many ways in which a particular number is obtained as the sum, for example 8 can be obtained with (2, 6),(6, 2),(3, 5),(5,3) and (4,4). The probability for the other numbers has also been determined in a similar way.
The probability of each of the 11 numbers is:
2: 1/36
3: 2/36
4: 3/36
5: 4/36
6: 5/36
7: 6/36
8: 5/36
9: 4/36
10: 3/36
11: 2/36
12: 1/36
The sum of the probabilities adds up to 1.
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