Suppose we have 2 fair 6-sided dice numbered from 1 to 6. If we roll them both, what is the probability that the two numbers shown sum to 7?

We find the number of ways where the two numbers on the dice rolled add up to 7.

We can have:

1 6

2 5

3 4

4 3

5 2

6 1

 

The total number of sums we can get is 6 x 6=36.

So the probability of rolling a sum of 6 is 6/36=1/6.