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Just as one die has six outcomes and two dice have 62 = 36 outcomes, the probability experiment of rolling three dice has 63 = 216 outcomes.

## 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%) |

## How many possible ways are there to roll a 4 with 2 dice?

Probabilities for the two dice

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

2 | 1 | 2.78% |

3 | 2 | 5.56% |

4 | 3 | 8.33% |

5 | 4 | 11.11% |

## How many outcomes are in the event of rolling a 2 each of the 3 times?

For each of the three choices there are 2 different outcomes. The total number of outcomes is begin{align*}2 times 2 times 2 = **8**end{align*}. This method of calculating the number of total outcomes can be stated as a general rule called the Counting Principle.

## What is the probability of getting a sum of 7 with two dice?

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**.