What is the probability of rolling a sum that is not a 7 or 11 with a pair of dice?

There are 6 ways to get a sum of seven

1+6, 2+5, 3+4, 4+3, 5+2 and 6+1

There are 2 ways to get a sum of eleven

5+6, 6+5

So there are a total of *8* ways to get a sum that *is* 7 or 11. You want the ways to get a sum that is *not* 7 or 11, so subtract from 36 (total ways to roll two dice).

28 ways (not a sum of 7 or 11)

36 total ways to roll two dice.

P(not 7 or 11) = 28/36 = 7/9

Here are the sums that are 7:

1-6

2-5

3-4

4-3

5-2

6-1

Count them.

Write down the sums that are 11. Count them.

The total of those two numbers is the number of outcomes that ARE 7 or 11. Since there are 36 possible outcomes, the outcomes that aren't 7 or 11 is 36 minus that number.

Probability = (# of outcomes that aren't 7 or 11) / (total # of possible outcomes)