Trial | Outcomes | Examples of Events |
---|---|---|

Rolling a die | There are 6 possible outcomes: {1, 2, 3, 4, 5, 6} | Rolling an even number: {2, 4, 6} Rolling a 3: {3} Rolling a 1 or a 3: {1, 3} Rolling a 1 and a 3: { } (Only one number can be rolled, so this outcome is impossible. The event has no outcomes in it.) |

## What are the possible outcomes when a dice is rolled?

For example, when a die is rolled, the possible outcomes are **1, 2, 3, 4, 5, and 6**. In mathematical language, an event is a set of outcomes, which describe what outcomes correspond to the “event” happening. For instance, “rolling an even number” is an event that corresponds to the set of outcomes {2, 4, 6}.

## When a dice is rolled There are 6 possible outcomes What is the likelihood of the dice landing a 3?

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 different outcomes are possible after rolling all six dice?

The number of possible outcomes is 66=**46656**.

## What is a rolling die?

“Die” is the singular form of “dice,” so “roll a **die” means rolling one**, and “roll the dice” means rolling two. See a translation.

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

You can see, only number **7** can be scored in each case, therefore 7 is the most common result, if you roll one dice and then another one.

## What is the probability of rolling a sum of 3?

We divide the total number of ways to obtain each sum by the total number of outcomes in the sample space, or 216. The results are: Probability of a sum of **3: 1/216 = 0.5%** Probability of a sum of 4: 3/216 = 1.4%

## What is the probability of not rolling a four when rolling a six-sided die?

In this case the probability of not rolling a 4 is 5/6 or approximately **83.33%**. This is because there are 5 numbers that are not a 4 on a standard six-sided die.

## What is the probability of getting a 7 when rolling 2 dice?

Probabilities for the two dice

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

7 | 6 |
16.67% |

8 | 5 | 13.89% |

9 | 4 | 11.11% |

10 | 3 | 8.33% |