Question

If two fair dice are rolled, what is the probability that a total showing is either even or less than eight?

How would I solve this question?

What are the steps?

Thanks

Answer 1

If you are doing more of these dice-rolling problems it might be a good idea to have a matrix for 2 dice showing rows and columns from 1 to 6, and sums as the entries of the matrix

you will see that there are 18 even sums and 18 odd sums.
For a sum of less than 8 we have:
1,6 1,5, 1,4 1,3 1,2 1,1 ---- 6 of them
2,5 2,4 2,3 2,2 2,1 ----5 of them
3,4 3,3 3,2 3,1 ------4 of them
4,3 4,2 4,1 -------- 3 of them
5,2 5,1 -------- 2 of them
6,1 -------- 1 more
but in this total of 21 , 12 are already counted in the odds
so P(odd or <8) = (18 + 21 - 12)/36
= 3/4