Final answer:
To find the outcomes where the sum of two rolled dice is greater than six, we list the possible outcomes and identify the ones that meet the condition. There are 21 outcomes in this event.
Step-by-step explanation:
To find the outcomes in the sample space where the sum of two rolled dice is greater than six, we can list all the possible outcomes and then identify the ones that meet the condition. Assuming we are rolling two standard six-sided dice, the sample space consists of 36 equally likely outcomes (6 outcomes for the first die multiplied by 6 outcomes for the second die).
When the sum of the two dice is greater than six, we are looking for the outcomes where the sum is 7, 8, 9, 10, 11, or 12. These outcomes include (1,6), (2,5), (2,6), (3,4), (3,5), (3,6), (4,3), (4,4), (4,5), (4,6), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6). So, there are a total of 21 outcomes in the event where the sum of the two rolled dice is greater than six.