**Contents**show

Roll a… | Probability |
---|---|

8 | 5/36 (13.889%) |

9 | 4/36 (11.111%) |

10 | 3/36 (8.333%) |

11 | 2/36 (5.556%) |

## What is the probability that the sum of rolling two fair six sided dice will be no more than 5?

Answer: If you roll two fair six sided dice what is the probability that the sum is 5 or lower? The easy way is to count outcomes. Of the 36 equally probable outcomes, 10 are less than or equal to 5, so the probability is **10/36 = 5/18**.

## What is the chance that rolling two six sided dice results in rolling 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**.

## What is the expected value of rolling 2 fair 6 sided dice?

For example, if a fair 6-sided die is rolled, the expected value of the number rolled is **3.5**. The expectation of the sum of two (independent) dice is the sum of expectations of each die, which is 3.5 + 3.5 = 7.

## When two fair six sided dice are rolled what is the probability that the sum of the numbers on the top faces of the dice is 6 but neither top face shows a 5?

Since there are 6 * 6 = 36 possible rolls of two dice, there are 18 rolls whose sum is even. So there are 6 possibilities for the sum to be 7. Thus, there are 18 + 6 = 24 possibilities for the sum to be even or 7. This gives a probability of 24/36 = **66.6%**.

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

Answer: The probability of rolling two dice and getting a sum of 4 is **1/12**. Let’s find how likely we get a sum of 4 when we roll two dice simultaneously. So, when we roll two dice there are 6 × 6 = 36 possibilities. When we roll two dice, the possibility of getting number 4 is (1, 3), (2, 2), and (3, 1).

## What is the probability of rolling a 5?

Two (6-sided) dice roll probability table

Roll a… | Probability |
---|---|

4 | 3/36 (8.333%) |

5 | 4/36 (11.111%) |

6 | 5/36 (13.889%) |

7 | 6/36 (16.667%) |

## What is the most common number to roll with 1 dice?

For four six-sided dice, the most common roll is **14**, with probability 73/648; and the least common rolls are 4 and 24, both with probability 1/1296. , 2, 3, and 4 dice. They can be seen to approach a normal distribution as the number of dice is increased.