# Rolling the dice...

### What are the most likely outcomes from rolling a pair of dice?

Assuming we have a standard six-sided die, the odds of rolling a particular value are 1/6. There is an equal probability of rolling each of the numbers 1-6. But, when we have two dice, the odds are not as simple. For example, there's only one way to roll a two (snake eyes), but there's a lot of ways to roll a seven (1+6, 2+5, 3+4).

Let's count how many ways there are to get each value, 2 through 12:

 Outcome List of Combinations Total 2 1+1 1 3 1+2, 2+1 2 4 1+3, 2+2, 3+1 3 5 1+4, 2+3, 3+2, 4+1 4 6 1+5, 2+4, 3+3, 4+2, 5+1 5 7 1+6, 2+5, 3+4, 4+3, 5+2, 6+1 6 8 2+6, 3+5, 4+4, 5+3, 6+2 5 9 3+6, 4+5, 5+4, 6+3 4 10 4+6, 5+5, 6+4 3 11 5+6, 6+5 2 12 6+6 1

If we want to calculate the probability of rolling, say, a five, we need to divide the number of ways to get 5 by the total possible combinations of two dice.

How many total combinations are possible from rolling two dice? Since each die has 6 values, there are $$6*6=36$$ total combinations we could get. If you add up the numbers in the total column above, you'll get 36.

So, we can calculate the probabilities of each outcome:

 Outcome Probability 2 1/36 = 2.78% 3 2/36 = 5.56% 4 3/36 = 8.33% 5 4/36 = 11.11% 6 5/36 = 13.89% 7 6/36 = 16.67% 8 5/36 = 13.89% 9 4/36 = 11.11% 10 3/36 = 8.33% 11 2/36 = 5.56% 12 1/36 = 2.78%