An Experiment Consists of Casting a Pair of Dice and Observing

question 229

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 falling uppermost on one die is a 2 and the number falling uppermost on the other die is greater than 2.
Express your answer using set notation.

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Definitions:

Margin Of Error

An indicator of the precision of an estimate or poll, expressing the range within which the true value lies with a specified level of probability.

Confidence

The degree of certainty or trust in a specific context, often used to refer to the level of certainty in statistical conclusions.

Confidence Interval

A band of numerical estimates, from sample data, seen as likely to include the value of an invisible population characteristic.

Sampling Distribution

The probability distribution of a given statistic based on many random samples from a specific population.