Final answer:
The complement of event E, where the sum of two rolled dice is divisible by 5, includes all outcomes where the sum is not divisible by 5. For standard six-sided dice, this includes sums of 2, 3, 4, 6, 7, 8, 9, 11, and 12, each with various dice combinations.
Step-by-step explanation:
The event E is defined as the sum of two rolled dice being divisible by 5. To find the complement of E, denoted as Ec, we must list the outcomes where the sum of the two dice is not divisible by 5. The possible sums that are divisible by 5 when two dice are rolled are 5, 10, 15, and 20. However, since we are rolling standard six-sided dice, the highest possible sum is 12 (when rolling two sixes), so the only relevant sums for event E are 5 and 10.
To list the outcomes in Ec, we consider all the other possible sums: 2, 3, 4, 6, 7, 8, 9, 11, and 12. There are several dice combinations that yield each of these sums:
- Sum of 2: (1,1)
- Sum of 3: (1,2), (2,1)
- Sum of 4: (1,3), (2,2), (3,1)
- Sum of 6: (1,5), (2,4), (3,3), (4,2), (5,1)
- Sum of 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)
- Sum of 8: (2,6), (3,5), (4,4), (5,3), (6,2)
- Sum of 9: (3,6), (4,5), (5,4), (6,3)
- Sum of 11: (5,6), (6,5)
- Sum of 12: (6,6)
These are all the outcomes where the sum is not divisible by 5, hence they are all part of the complement of event E.