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## What is the probability that you would obtain a sum of 7 or a sum of 11 on the first roll?

For example, since a 7 or an 11 is a winner on the first roll and their probabilities are 6/36 and 2/36, the probability of winning on the first roll is 6/36+2/36=**8/36**.

## How many ways can you roll a 7 with 3 dice?

When three different numbers form the partition, such as 7 = 1 + 2 + 4, there are **3!** (3x2x1) different ways of permuting these numbers. So this would count toward three outcomes in the sample space.

## What is the probability of rolling a 7 or 11 with two dice?

The probability of winning on the first roll is the probability of rolling 7 or 11, which is 1/6 plus 1/18, which equals to **2/9**. Suppose we roll 4 on the first roll (the probability of rolling 4 is 1/12). On each successive roll the probability of rolling 7 is 1/6 and the probability of rolling 4 is 1/12.

## What is the probability of rolling a sum larger than 10?

Since there are a total of 6 x 6 = 36 outcomes, then the probability that the sum will be greater than 10 is **3/36 = 1/12**.

## What is the probability of getting a sum of 2 if a pair of dice is rolled?

The answer is the following: the combinations (1,3) and (2,2) are not equiprobable. We have a probability of 1/6 that the first die rolls 2, and a probability of 1/6 that the second die rolls 2, thus making a combination (2,2) with the probability **1/36**.

## What is the probability of 3 dice?

Two (6-sided) dice roll probability table

Roll a… | Probability |
---|---|

3 | 3/36 (8.333%) |

4 | 6/36 (16.667%) |

5 | 10/36 (27.778%) |

6 | 15/36 (41.667%) |

## How many ways can you roll a 6 with two dice?

Probabilities for the two dice

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

4 | 3 | 8.33% |

5 | 4 | 11.11% |

6 |
5 |
13.89% |

7 |
6 |
16.67% |

## What is the probability of rolling a 6 with 3 dice?

So, there are 125 out of 216 chances of a 6 NOT appearing when three dice are rolled. Simply subtract 125 from 216 which will give us the chances a 6 WILL appear when three dice are rolled, which is **91**. 91 out of 216 or 42.1 %.