# How many different sums can you get from rolling two dice?

Contents

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 62 = 36 outcomes, the probability experiment of rolling three dice has 63 = 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.

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First coin Second coin outcome
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## 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?

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 .

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