The last die may have six values. For each of these six values, the second- to-last die may have six values. Thus, we have 6·6 = 36 possible outcomes for the last two dice. By extension, we have a total of 65 = 7776 possible outcomes for all five dice.

## How many possible outcomes are there when five dice are rolled in which at least one dice shows 6?

= P(A) + P(B) – P(A and B) Let’s assume we are rolling five fair six-sided dice, numbered 1 through 6. The total number of possible outcomes of a roll of five dice is 6^5 = **7,776**.

## What is the probability of rolling 5 dice and getting at least one matched pair?

The probability that there is at least one pair is 1−P=4954. and so the probability is **2554**.

## How many different outcomes are there that would show a 5 on at least one of the dice?

The possible outcomes with at least one die showing 5 in this case is **11**. Generally, 2n-1 is an appropriate formula where n is the number of sides on the dice. Suppose the dice have 9 sides each, we have: 2(9)-1= 17, this implies that there are 17 possible outcomes having at least one die showing 5.

## What is the probability of rolling a 5 on a 6-sided dice?

Two (6-sided) dice roll probability table

Roll a… | Probability |
---|---|

5 | 10/36 (27.778%) |

6 | 15/36 (41.667%) |

7 | 21/36 (58.333%) |

8 | 26/36 (72.222%) |

## How many ways are there to roll at least one 6?

So counting them, we get 11 of the possible **36 outcomes** of which at least one 6 is rolled. Now simply express this probability as a fraction! P(X=1) = P(the first dice has 6, the second hasn’t) + P(the second dice has 6, the first one hasn’t) = 1/6 * 5/6 + 5/6 * 1/6 = 5/ 36 + 5/36 = 5/18 = 0.2778.

## What are the odds of getting 5 Yahtzees in one game?

The probability of rolling five of a kind of any other number is also **1/7776**. Since there are a total of six different numbers on a die, we multiply the above probability by 6. This means that the probability of a Yahtzee on the first roll is 6 x 1/7776 = 1/1296 = 0.08 percent.

## Is Yahtzee a skill or luck?

As with all games, **players typically need elements of both skill and luck**. However, some games are known for needing more skill than others. In a 2020 survey conducted by YouGov, 49 percent of respondents in the United States stated that Yahtzee was a game of luck rather than skill.

## What is the probability of rolling a 5 and then rolling a second 5 on a pair of dice?

There is a 16 probability of getting a 2 on the first roll and **a 16 probability** of getting a 5 on the second roll.