An Experiment Consists of Casting a Pair of Dice and Observing

question 130

Essay

An experiment consists of casting a pair of dice and observing the number that falls uppermost on each die. We may represent each outcome of the experiment by an ordered pair of numbers, the first representing the number that appears uppermost on the first die and the second representing the number that appears uppermost on the second die. Consider the 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)}
Determine the event that the number that falls uppermost on the first die is less than the number that falls uppermost on the second die.
Express your answer using set notation.

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Definitions:

Task Clarity

The extent to which the objectives, goals, and requirements of a specific task are clearly understood by those expected to perform it.

Role Definition

The clarification of an employee's or individual's job responsibilities, expectations, and duties within an organization or group.

Innovate

To innovate means to introduce new methods, ideas, or products; the act of creating something original and more effective.

Problem-solving Team

A group of individuals working together to find a solution to a specific issue or challenge.