When two dice are rolled, each die has six faces, numbered 1 through 6. However, we are only interested in the event where both dice show an even number.
First, let's identify the even numbers on a standard die: the even numbers are 2, 4, and 6. Thus, each die has 3 even numbers.
When focusing on one die, the number of possible outcomes that result in an even number is 3.
Since the result of one die is independent of the result of the other die, we can find the total number of favorable outcomes (where both dice show even numbers) by multiplying the number of favorable outcomes for the first die by the number of favorable outcomes for the second die.
For the first die, there are 3 favorable outcomes (2, 4, 6).
For the second die, there are also 3 favorable outcomes (2, 4, 6).
Therefore, the size of the sample space for the event that both dice show even numbers is:
[tex]\[ 3 \times 3 = 9 \][/tex]
So, the size of the sample space that corresponds to the event that both dice are even is [tex]\( \boxed{9} \)[/tex].
