**Contents**show

## What are the possible sums when 2 dice are rolled?

Note that there are **36 possibilities for (a,b)**. This total number of possibilities can be obtained from the multiplication principle: there are 6 possibilities for a, and for each outcome for a, there are 6 possibilities for b. So, the total number of joint outcomes (a,b) is 6 times 6 which is 36.

## When a pair of dice is rolled what is the probability that the sum of the dice is 6 Given that the outcome is not 11?

Answer: The probability of rolling a sum of 6 with two dice is **5/36**. Let’s solve this step by step.

## What is the probability that if we roll 2 dice the sum is 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**.

## When two dice are rolled what is the probability that the two numbers are have sum equal to 8?

Probabilities for the two dice

Total | Number of combinations | Probability |
---|---|---|

8 | 5 |
13.89% |

9 | 4 | 11.11% |

10 | 3 | 8.33% |

11 | 2 | 5.56% |

## When a pair of dice is rolled what is the probability of getting a sum of 10 or a pair of odd number?

When you consider the sum being 10, there are only 3 combinations. So, the probability of getting a 10 would be **3/36 = 1/12**.

## When a pair of dice is rolled what is the probability that the sum of the dice is given that the outcome is not?

The probability of any number occurring is 1 in 36 or 1 / 36. Then the probability an 8 will not occur is: 1 – 5 / 36 or **31 / 36**. I could have added up all of the ways an 8 could not occur such as: 1 / 36 + 1 / 36 … 1 / 36 = 31 / 36, but that is the hard way.