Final answer:
When two six-sided dice are rolled, the sample space consists of 36 possible events, determined by multiplying the 6 outcomes of one die with the 6 outcomes of the other die.
Step-by-step explanation:
Sample Space of Two Dice
When two fair six-sided dice are rolled, the sample space consists of 36 possible events. Each die has six faces, and since the dice are distinct, you can roll a 1 on the first die and a 1 on the second die as one event (1, 1), a 1 on the first die and a 2 on the second die as another event (1, 2), and so on until you reach the event of rolling a 6 on the first die and a 6 on the second die (6, 6).
To calculate the total number of possible outcomes, you multiply the number of outcomes for one die (which is 6) by the number of outcomes for the other die (also 6). Therefore, 6 outcomes from the first die times 6 outcomes from the second die equals 36 possible outcomes in the sample space.
For example, if you roll two dice, some of the possible outcomes in the sample space are (1,1), (1,2), (2,1), and (2,2), up to (6,6).