An Experiment Consists of Casting a Pair of Dice and Observing

question 235

Multiple Choice

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 greater than the number that falls uppermost on the second die.

• A) {(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)}
• B) {(1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (3, 2), (4, 2), (5, 2), (6, 2), (4, 3), (5, 3), (6, 3), (5, 4), (6, 4), (5, 6)}
• C) {(2, 1), (3, 1), (4, 1), (5, 1), (6, 1), (2, 3), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 5), (6, 4), (6, 5)}
• D) Ø

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Definitions:

Given

A term used in mathematics and logic to denote something that is assumed to be true or is provided as part of the problem statement.

Simplify

To simplify a mathematical expression or problem to its most basic version.

Competitive Output Markets

Markets where multiple firms sell similar or identical products, and prices are determined through competition among sellers.

Exponent

In mathematics, a number indicating how many times a base is to be multiplied by itself.