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Let E be the event where the sum of two rolled dice is less than 8. List the outcomes in Ec.

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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.

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