Question

A pair of fair dice is rolled.

(a) What is the sample space of this experiment?

(b) Describe the set that corresponds to the event that the first die lands on a strictly higher value than the second die.

Answer 1

(a)

The sample space for this experiment is as shown below:

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

There are total: 6*6 = 36 outcomes

(b)

The set that corresponds to the event that the number appearing on the first die is greater than that on the second is as shown below:

{(2,1), (3,1), (4,1), (5,1), (6,1),(3,2), (4,2), (5,2), (6,2),(4,3), (5,3), (6,3),(5,4), (6,4),(6,5) }

There are total 15 outcomes.