For three six-sided dice, the most common rolls are 10 and 11, both with probability 1/8; and the least common rolls are 3 and 18, both with probability 1/216. 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.

## What is the most likely sum when rolling 3 dice?

The smallest possible sum occurs when all of the dice are the smallest, or one each. This gives a sum of three when we are rolling three dice. The greatest number on a die is six, which means that the greatest possible sum occurs when all three dice are sixes. The sum of this situation is **18**.

## What is the expected sum of three dice?

There are 216 possible outcomes when three dice are thrown. Since the dice are ‘fair’ each of them has an equal probability. There are 27 different combinations that produce a sum of **10** (1–3–6, 2–2–6, etc).

## 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%) |

## When 3 dice are rolled find the probability of getting a sum of 8?

Giving a total of 21 different number combinations (out of 216 possible combinations) which sum to 8. So there are (21)/(216) possible correct combinations which meet the demands of the question. This gives a probability of (21)/(216) or 9.72222% or **0.097222** of getting a sum of 8 when 3 die are thrown.

## What is a six-sided die?

The most common type of die is a **six-sided cube with the numbers 1-6 placed on the faces**. The value of the roll is indicated by the number of “spots” showing on the top. For the six-sided die, opposite faces are arranged to always sum to seven.

## What is the probability of rolling a sum of 12 on a six sided dice?

Probabilities for the two dice

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

10 | 3 | 8.33% |

11 | 2 | 5.56% |

12 | 1 |
2.78% |

Total | 36 | 100% |

## What is the probability of rolling a sum of 8 with two dice?

There are 36 outcomes in total. Five of them (2,6), (3,5), (4,4), (5,3) and (6,2) result in sum 8. So, assuming all outcomes are equiprobable, the answer is **5/36**.

## What is the probability of getting a sum of 7 when two dice are thrown?

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 probability that two dice sum to 8 when the first dice is 3?

The total number of ways to roll an 8 with 3 dice is therefore 21, and the probability of rolling an 8 is **21/216**, which is less than 5/36. heads out of 20 is (20 10 ) /220 ≈ 17.6%.