# What is the sample space when rolling 3 dice?

## What is the sample space when rolling 3 dice?

When three dice are rolled sample space contains 6 × 6 × 6 = 216 events in form of triplet (a, b, c), where a, b, c each can take values from 1 to 6 independently. Therefore, the number of samples is 216.

### What is the sample space of rolling a dice?

The size of the sample space is the total number of possible outcomes. For example, when you roll 1 die, the sample space is 1, 2, 3, 4, 5, or 6. So the size of the sample space is 6. Then you need to determine the size of the event space.

**What is the probability of rolling 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 elements are in the sample space of tossing 3 different colored dice?**

six elements

Rolling a die. There are six possible outcomes and the sample space consists of six elements: {1, 2, 3, 4, 5, 6}.

## What are the total number of outcomes when 3 dice are thrown simultaneously?

216

Solution: Three different dice are thrown at the same time. Therefore, total number of possible outcomes will be 63 = (6 × 6 × 6) = 216.

### What is sample space with examples?

Sample space is all the possible outcomes of an event. Sometimes the sample space is easy to determine. For example, if you roll a dice, 6 things could happen. You could roll a 1, 2, 3, 4, 5, or 6.

**What is the sample space of an event?**

The sample space of a random experiment is the collection of all possible outcomes. An event associated with a random experiment is a subset of the sample space. The probability of any outcome is a number between 0 and 1.

**What is the formula for sample space?**

The sample space is S = {HH,HT,TH,TT}. E = {HH,HT} is an event, which can be described in words as ”the first toss results in a Heads. Example 4 Tossing a die twice. The sample space is S = {(i, j) : i, j = 1,2,…,6}, which contains 36 elements. ”The sum of the results of the two toss is equal to 10” is an event.

## When 3 dice are tossed simultaneously how many outcomes can there be?

Solution: Three different dice are thrown at the same time. Therefore, total number of possible outcomes will be 63 = (6 × 6 × 6) = 216.

### When 3 dice are rolled what is the probability of getting a sum of 15?

5/108

If three dice are thrown simultaneously then probability of getting a sum of 15 is 5/108 .