The sample space of two dice is
We look for combinations such that the sum of the two dice is greater than 10.
The three samples (6,5), (5,6), and (6,6) make the event E. Therefore, the complement of E is the set where in the sum of two dice is not greater than 10.
[tex]\begin{gathered} E^C=\{(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),(6,1),(6,2),(6,3),(6,4)\} \end{gathered}[/tex]
