Rolling two six-sided dice: Each die has 6 equally likely outcomes, so the sample space is 6 • 6 or 36 equally likely outcomes.

## How do you find the sample space of two dice?

You could write the sample space another way, **by just adding up the two dice**. For example [1][1] = 2 and [1][2] = 3. That would give you a sample space of {2, 3, 4, 6, 7, 8, 9, 10, 11, 12}.

## What are all the possible outcomes of rolling 2 dice?

Why do we know, without listing them all, that there are **36 outcomes** when two dice are rolled? We can view the outcomes as two separate outcomes, that is, the outcome of rolling die number one and the outcome of rolling die number two.

## What is the probability of spinning a 2 and rolling a 3?

There are 8 numbers for that spinner so the probability of getting a 2 out of 8 numbers is 1/8. There are 6 sides for a die so the probability of getting a 3 out of 6 sides is 1/6. Since spinning a spinner and rolling a die are Independent, the probability of both happening is 1/8 times 1/6 which is **1/48**.

## When two sided dice are rolled There are 36 possible outcomes?

Every time you add an additional die, the number of possible outcomes is multiplied by 6: 2 dice 36, 3 dice 36*6 = **216 possible outcomes**.

## What is the sample size for rolling two 6 sided dice?

The Fundamental Counting Principle

Rolling two six-sided dice: Each die has 6 equally likely outcomes, so the sample space is **6 • 6 or 36 equally likely outcomes**.

## What is the probability of rolling a four with a six sided die?

Two (6-sided) dice roll probability table

Roll a… | Probability |
---|---|

4 | 3/36 (8.333%) |

5 | 4/36 (11.111%) |

6 | 5/36 (13.889%) |

7 | 6/36 (16.667%) |

## What is the sample space of 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.