Note that there are 36 possibilities for (a,b). This total number of possibilities can be obtained from the multiplication principle: there are 6 possibilities for a, and for each outcome for a, there are 6 possibilities for b. So, the total number of joint outcomes (a,b) is 6 times 6 which is 36.

## How many different sums are possible in the dice activity?

**Possible** Outcomes and **Sums**

Just as one die has six outcomes and two **dice** have 6^{2} = 36 outcomes, the probability experiment of rolling three **dice** has 6^{3} = 216 outcomes.

## How many number of total outcomes can you have if your events are rolling 2 dice and 2 coins?

Rolling two six-sided dice: Each die has 6 equally likely outcomes, so the sample space is 6 • 6 or **36** equally likely outcomes. Flipping three coins: Each coin has 2 equally likely outcomes, so the sample space is 2 • 2 • 2 or 8 equally likely outcomes.

…

First coin | Second coin | outcome |
---|---|---|

T | T | TT |

## How many ways can two dice be rolled such that their sum is not more than 10?

11, 2 ways = (5+6), (6+5). 12, 1 way = (6+6). As you can see there are 2+1 = **3 ways** of getting more than 10 and 33 ways of getting 10 or less.

## 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 different sums are possible with 10 dice?

These multiset permutations can also be considered as the number of **possible different** anagrams of a 7-letters word, in which only two **different** characters (⊕ and |) are used. Later we’ll use this concept to find the number of ways in which (say) **10 dice** can yield a **sum** of (say) 31.

## Which is more likely never getting a 6 when rolling a fair die six times or never getting a double 6 when rolling a pair of fair dice 36 times?

More likely is never getting a double 6 when rolling a pair of fair dice 36 times. Because the probability of getting 6 with one die rolled 6 times is **1/6**.

## What is the probability of getting a sum of 20 when tossing 2 dice?

Answer Expert Verified

The maximum sum that we can get when we roll 2 dice is 12. So, the probability of getting 20 is obviously .

## What are the odds of rolling a 12 with two dice?

Probabilities for the two dice

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

10 | 3 | 8.33% |

11 | 2 | 5.56% |

12 | 1 |
2.78% |

Total | 36 | 100% |

## What is the probability of rolling a 2 or higher on a six sided die?

The probability of rolling a 2 on a 6-sided dice is **16** . The probability of rolling two 2s on two 6-sided die is, by the multiplication principle, 16×16=136 .