To determine the size of the sample space when two 6-sided dice are rolled, let's go through the problem step-by-step.
Each die has 6 faces, numbered from 1 to 6. When rolling two such dice, the outcome on each die is independent of the other.
1. For the first die, there are 6 possible outcomes (1, 2, 3, 4, 5, 6).
2. Likewise, for the second die, there are also 6 possible outcomes (1, 2, 3, 4, 5, 6).
The total number of possible outcomes when rolling two dice is found by multiplying the number of possible outcomes on the first die by the number of possible outcomes on the second die. This is because every face of the first die can pair with every face of the second die.
So, the size of the sample space is calculated as follows:
[tex]\[
6 \, \text{(outcomes for the first die)} \times 6 \, \text{(outcomes for the second die)} = 36
\][/tex]
Therefore, the size of the sample space when two 6-sided dice are rolled is [tex]\( \boxed{36} \)[/tex].
