**Contents**show

## What is the probability of rolling a total of 8 on two dice?

Probabilities for the two dice

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

5 | 4 | 11.11% |

6 | 5 |
13.89% |

7 | 6 | 16.67% |

8 | 5 | 13.89% |

## Which is more likely rolling a total of 9 when two dice are rolled or rolling a total of 9 when three dice are rolled?

Which is more likely, rolling a total of 9 when two dice are rolled or rolling a total of 9 when three dice are rolled? Answer: 9 = 3+6 = 4+5 = 5+4 = 6+3, — 4 ways to get total of 9 points rolling two dice, so the probability that the outcome is 9 points is: 4/(6*6) = 1/9 = **0.111**.

## What is the probability of getting a total of 6 or 8 on a roll of a pair of dice?

Two (6-sided) dice roll probability table

Roll a… | Probability |
---|---|

6 | 15/36 (41.667%) |

7 | 21/36 (58.333%) |

8 | 26/36 (72.222%) |

9 | 30/36 (83.333%) |

## What is the expected sum of the numbers that appear when three fair dice are rolled?

The expectation of the sum is the sum of the expectation values for the three dice. But since they are all fair dice, they have the same expectation values. Hence **E(S) = 3 E(s1)**. The outcomes for a single fair die are 1,2,3,4,5,6 each with probability 1/6.

## What are the outcomes of rolling 2 dice?

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.

## What is the probability of rolling a total that is neither 7 nor 11?

Therefore Probablity of sum neither 7 nor 11 is **7/9**.

## What is the probability that sum of outcomes on pair of dice is equal to 8?

So the probability is the sum of the five individual probabilities which is 5*(1/36)= **5/36**. Therefore the probability that we get the sum as 8 when two dice are thrown is 5/36.

## What is the probability of getting a sum of 9 when two dice are thrown simultaneously?

probability **4/36 or 1/9**. In order to get a sum of 9 with two dice, you would have to roll the pairs 4 & 5, 5 & 4, 3 & 6, or 6 & 3.

## What is the probability of getting 1 and 5 If a dice is thrown once?

So they are mutually exclusive events, therefore their probabilities add to 1. By symmetry we expect that each face is equally likely to appear and so each has probability = **1/6**. The outcome of a 5 is one of those events and so has probability = 1/6 of appearing.