Dice Sum Possibilities
Probability
Level
2
Sam rolls 2 standard 6-sided dice and writes down the sum of the top faces. How many different values could the sum have?
The answer is 11.
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The sum ranges from 1 + 1 = 2 to 6 + 6 = 1 2 , and we can obtain every integer in-between. Hence, there are 1 2 − 2 + 1 = 1 1 possible totals.
For completeness, we can list them out as 1 + 1 = 3 , 1 + 2 = 3 , 1 + 3 = 4 , 1 + 4 = 5 , 1 + 5 = 6 , 1 + 6 = 7 , 2 + 6 = 8 , 3 + 6 = 9 , 4 + 6 = 1 0 , 5 + 6 = 1 1 , 6 + 6 = 1 2 .