Question

Let E be the event where the sum of two rolled dice is greater than or equal to 11. List the outcomes in E^c

Answer 1

We are given that "E" is the event that the sum of two dices is greater or equal to 11. We are asked about the complement of "E" which is represented as:

`E^c`

The complement of "E" would be the event where the sum of the two dices is less than 11, therefore, the possible outcomes are the following. We will use the notation in the form of ordered pairs (x, y) where "x" is a number in the first dice and "y" the number in the second dice:

`\begin{gathered} (1,1)\colon(1,2)\colon(1,3)\colon(1,4)\colon(1,5)\colon(1,6)_{} \\ (2,1)\colon(2,2)\colon(2,3)\colon(2,4)\colon(2,5)\colon(2,6) \\ (3,1)\colon(3,2)\colon(3,3)\colon(3,4)\colon(3,5)\colon(3,6) \\ (4,1)\colon(4,2)\colon(4,3)\colon(4,4)\colon(4,5)\colon(4,6) \\ (5,1)\colon(5,2)\colon(5,3)\colon(5,4)\colon(5,5) \\ (6,1)\colon(6,2)\colon(6,3)\colon(6,4) \end{gathered}`

These are the possible outcomes for the sum of the two dices being less than 11.