An Experiment Consists of Casting a Pair of Dice and Observing

question 159

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 second die is double that of the number that falls on the first die.
Express your answer using set notation.

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Definitions:

Government Efforts

Initiatives or actions taken by a government to address societal issues, regulations, or economic policies.

Private Efforts

Actions undertaken by individuals or private organizations rather than by the government or public entities to achieve a particular goal.

Political Corruption

The misuse of public power by government officials for private gain, often compromising the interests and rights of citizens.

Institutional Problem

Challenges and issues within established organizations that hinder their effectiveness or goals.