# What is the probability of not rolling a sum of 2 4 or 6 with two fair dice?

There are 36 possible outcomes when throwing 2 dices : 6 for the first dice (1,2,3,...6) and 6 for the second dice

Let say that in the sums below the first number is the result of the first dice and the second number is for the result of the second dice:

2 = 1 + 1: 1 possibility

4 = 2 + 2 = 1 + 3 = 3 + 1: 3 possibilities

6 = 1 + 5 = 5 + 1 = 2 + 4 = 4 + 2 = 3 +3: 5 possibilities

1 + 3 + 5 = 9 possibilities to get 2 or 4 or 6

So the probability to get a sum of 2 or 4 or 6 is 9/36=1/4

And the probabilty of NOT rolling a sum of 2 or 4 or 6 is 1-1/4=3/4