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Q: What is the probability of rolling a sum of 10 in two dice?

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Zero is the probability of rolling a sum of 15 on two fair dice; the maximum value is 12.

The probability of not rolling a sum of six with two fair dice is 1 minus the probability of rolling a sum of six. There are 36 permutations of rolling two dice. Of these, five sum to six, 1+5, 2+4, 3+3, 4+2, and 5+1. The probability, then of rolling a sum of six is 5 in 36. The probability, then of not rolling a sum of six is 31 in 36, or about 0.8611.

5 in 36

The probability is 1.

The probability is 29/36.

The probability is 1, if the dice are rolled often enough.

1 in 18.

It is 0.02777... recurring.

The probability of rolling a sum of 12 in a single roll of two dice is 1 in 36, or about 0.0278.

35/36

The probability of rolling 12 with 2 dice is 1 in 36. The probability of not rolling 12 with 2 dice is 35 in 36.

Since there are two permutations of two dice that sum to 11, (5-6) and (6-5), and since there are 36 permutations of rolling two dice, the probability of not rolling a sum of 11 is 34 in 36, or 17 in 18, or about 0.9444.

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