Question

Use a tree diagram or table to determine the sample space for an experiment in which an eight-sided number cube is rolled twice. How many different possible outcomes are there?

Answer 1

Let the ordered pair (a, b) denote the result of the first roll a and the second roll b, where a, b ∈ {1,2,3,4,5,6,7,8}.

Sample space S = {(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),
(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),
(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(3,7),(3,8),
(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(4,7),(4,8),
(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(5,7),(5,8),
(6,1),(6,2),(6,3),(6,4),(6,5),(6,6),(6,7),(6,8),
(7,1),(7,2),(7,3),(7,4),(7,5),(7,6),(7,7),(7,8),
(8,1),(8,2),(8,3),(8,4),(8,5),(8,6),(8,7),(8,8)}

Number of possible outcomes = 8 × 8 = 64.