Answer
The total number of outcomes is equal to 36 $(n(S) = 36)$
The elements of the event $E$ are: $E = \{ (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)\}$
And the probability of $E$ is equal to $\frac 1 6$
Work Step by Step
Two distinguishable dice are rolled:
1. A dice roll will result in a number between 1 and 6:
$S = \{(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\}$
Therefore: $n(S) = 36$, which is the total number of outcomes.
2. The set: "E" will have all the outcomes that add to 7:
$E = \{ (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)\}$
$n(E) = 6$
3. Calculate the probability:
$P(E) = \frac{n(E)}{n(S)} = \frac 6 {36} = \frac 1 6$
