We have an event E that represent the outcomes where the sum of the two rolled dice is even.
This includes all the combinations when both dices are even or both dices are odd.
We have to list the outcomes for Ec, the complement of E. This event Ec will represent all the outcomes where the sum of the two dices is odd.
All outcomes where one dice is even and the other is odd are part of Ec.
Then, we can list them as:
(1,2), (1,4), (1,6)
(2,1), (2,3), (2,5)
(3,2), (3,4), (3,6)
(4,1), (4,3), (4,5)
(5,2), (5,4), (5,6)
(6,1), (6,3), (6,5)
This represents half of the sample space. The other half corresponds to outcomes that are part of event E.
Answer: all the outcomes that correspond to Ec are (1,2), (1,4), (1,6), (2,1), (2,3), (2,5), (3,2), (3,4), (3,6), (4,1), (4,3), (4,5), (5,2), (5,4), (5,6), (6,1), (6,3) and (6,5).