Answer:
[tex]\frac{5}{9}\approx0.556[/tex]
Step-by-step explanation:
A pair of dice is rolled so the outcome space will be.
[tex]S= \{(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)\}[/tex]
Total number of elements [tex]=36[/tex]
Possible outcomes in which sum is less than [tex]6[/tex] or greater than [tex]8[/tex]
[tex]S_{1} = \{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(3,1),(3,2),(3,6),\\(4,1),(4,5),(4,6),(5,4),(5,5),(5,6),(6,3),(6,4),(6,5),(6,6)\}[/tex]
Number of element in this space [tex]=20[/tex]
P(sum is less than [tex]6[/tex] or greater than [tex]8[/tex])
[tex]=\frac{Favourable\ outcomes}{total\ outcomes} \\=\frac{20}{36}\\ =\frac{5}{9}[/tex]
