Question

You roll a pair of fair six-sided dice. The sample space of 36 possible outcomes is shown below. Based on this information, answer the following questions.

Answer 1

All the 36 outcomes are equally likely.

Explanation:

The sample space of rolling a single six-sided dice is:

S = {1, 2, 3, 4, 5, 6}

Then the sample space of rolling a pair of six-sided dice is:

S₁ = {(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)}

All the 36 outcomes are equally likely, i.e. all the outcomes has the same probability of success,
`(1)/(36)`.