Question

Suppose you roll a six-sided die two times hoping to get two numbers whose sum is even. What is the sample space? How many favorable outcomes are there?

Answer 1

1. the first throw you have six possible outcomes. Each of those can be followed by another six outcomes on the second through, so there are 6x6 = 36 possible outcomes - though of course many are duplicates, but you get a probability you have to count them.

As for which are favourable. Any pair of even numbers, any pair of odd numbers, but not an even/odd or an odd/even.

Answer 2

The sample space has 36 possible combinations of numbers. These can be set out in column form as follows:
6,6 5,6 4,6 3,6 2,6 1,6
6,5 5,5 4,5 3,5 2,5 1,5
6,4 5,4 4,4 3,4 2,4 1,4
6,3 5,3 4,3 3,3 2,3 1,3
6,2 5,2 4,2 3,2 2,2 1,2
6,1 5,1 4,1 3,1 2,1 1,1