Final answer:
The complement of event E, where the sum of two dice is less than 8, includes all dice combinations that result in a sum of 8 or more. These outcomes are pairs that add up to 8, 9, 10, 11, or 12.
Step-by-step explanation:
The complement of event E, denoted as Ec, consists of all outcomes where the sum of two rolled dice is 8 or greater. Since standard dice have six sides with values 1 through 6, the outcomes in Ec are the pairs of numbers that add up to 8, 9, 10, 11, or 12. These pairs are:
- (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) - These all sum to 8.
- (3, 6), (4, 5), (5, 4), (6, 3) - These sum to 9.
- (4, 6), (5, 5), (6, 4) - These sum to 10.
- (5, 6), (6, 5) - These sum to 11.
- (6, 6) - This sums to 12.
The probability of each of these outcomes is 1/36, given that we are rolling two fair six-sided dice and each die is independent of the other.