Let"s make a table of all possible sums of 2 dice, putting values of the first die in the far left column and also worths of the second die in the height 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 initially die and also 6 for the second, we have a complete of 6 x 6 = 36 feasible rolls for both dice.

In the table above, we view that tbelow are six possible combinations that give us a amount of 7, which suggests that the probcapability of rolling a 7 is 6 / 36 = 1/6.

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

Similarly, tbelow are 5 possible combicountries that offer a amount of 8, so P(sum = 8) = 5/36.

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

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

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

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

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