# Chapter 11 - 11.7 - Probability - 11.7 Exercises - Page 834: 26

$P(E)=\frac{5}{12}$

#### Work Step by Step

All the possible outcomes (sample space): $S=[(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)]$ We have that the total number of possible outcomes in the sample space is: $N(S)=36$ We want the sum to be at least 8 (the event): $E=[(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,3),(5,4),(5,5),(5,6),(6,2),(6,3),(6,4),(6,5),(6,6)]$ $N(E)=15$ $P(E)=\frac{N(E)}{N(S)}=\frac{15}{36}=\frac{5}{12}$

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