Let E be the event where the sum of two rolled dice is divisible by 4.
First, let us list all the possible outcomes when we roll two dice.
[ (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6) ]
These are all possible outcomes when we roll two dice. (total 36)
The event E means only those outcomes where the sum of two dice is divisible by 4.
But we need to find out the complement of event E.
This means all remaining outcomes by subtracting the outcomes of event E from the total outcomes.
The outcomes of event E are
E = [ (1, 3), (2, 2), (2, 6), (3, 1), (3, 5), (4, 4), (5, 3), (6, 2), (6, 6) ]
So, these are the outcomes where the sum is divisible by 4. (total 9)
The complement of event E is all the remaining outcomes without the above outcomes.
Complement of E = [ (1, 1), (1, 2), (1, 4), (1, 5), (1, 6), (2, 1), (2, 3), (2, 4), (2, 5), (3, 2), (3, 3), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 5), (4, 6), (5, 1), (5, 2), (5, 4), (5, 5), (5, 6), (6, 1), (6, 3), (6, 4), (6, 5) ]
Therefore, the above are the possible outcomes of the event E complement.
These outcomes basically represent the condition that the sum of two rolled dice is not divisible by 4.
