Let"s make a table of all possible sums of two dice, putting values of the first die in the far left column and values of the second die in the top row. We"ll put the corresponding sums in the table:

_ 1 2 3 4 5 6

1 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12

So with 6 possible rolls for the first die and 6 for the second, we have a total of 6 x 6 = 36 possible rolls for both dice.

In the table above, we see that there are six possible combinations that give us a sum of 7, which means that the probability of rolling a 7 is 6 / 36 = 1/6.

You are watching: What is the theoretical probability of rolling a sum of 10

Similarly, there are five possible combinations that give a sum of 8, so P(sum = 8) = 5/36.

Four combinations give a sum of 9, so P(sum = 9) = 4 / 36 = 1/9.

Three combinations give a sum of 10, so P(sum = 10) = 3 / 36 = 1/12

Two combinations give a sum of 11, so P(sum = 11) = 2 / 36 = 1/18

And finally, only both dice rolled as sixes give a sum of 12, so P(sum = 12) = 1/36.


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