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

One 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 favorable. Any pair of even numbers, any pair of odd numbers, but not an even/odd or an odd/even.