# What is the probability of not rolling a sum of 5 with two fair dice?

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## What is the probability of rolling a sum of 5 on 2 dice?

Probabilities for the two dice

Total Number of combinations Probability
2 1 2.78%
3 2 5.56%
4 3 8.33%
5 4 11.11%

## What is the probability of not rolling 5?

Probability of rolling less than certain number with one die

Roll less than a… Probability
3 2/6 (33.33%)
4 3/6 (50%)
5 4/6 (66.667%)
6 5/6 (83.33%)

## What is the probability of not rolling a sum of 4 with two fair dice?

There are six faces for each of two dice, giving 36 possible outcomes. If the two dice are fair, each of 36 outcomes is equally likely. Three outcomes sum to 4: (1+3), (2+2) and (3+1). Probability of getting a sum of 4 on one toss of two dice is 3/36, or 1/12.

## What is the probability that the sum are 5 and 7?

Now, the probability of a sum of 5 is 1/9, and the probability of a sum of 7 is 1/6.

## What is the probability of rolling 2 dice and getting a sum of 7?

For each of the possible outcomes add the numbers on the two dice and count how many times this sum is 7. If you do so you will find that the sum is 7 for 6 of the possible outcomes. Thus the sum is a 7 in 6 of the 36 outcomes and hence the probability of rolling a 7 is 6/36 = 1/6.

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