Explanation Given Information: The set contains all outcomes of rolling two indistinguishable dice. The sum of the two numbers on the dice is 6. Consider the provided set with all outcomes of rolling two indistinguishable dice to be S . Here the set of outcomes for rolling a dice is from 1 to 6. That is A = { 1 , 2 , 3 , 4 , 5 , 6 } . Since, the dice are distinguishable, thus, the sample space for the toss of two indistinguishable dice is A × A = { 1 , 2 , 3 , 4 , 5 , 6 } ⋅ { 1 , 2 , 3 , 4 , 5 , 6 } = { ( 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 ) } When the dice are indistinguishable, the order of the numbers that come up, do not matter

7th Edition

ISBN: 9781337280426

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

Question

Chapter 6.1, Problem 13E

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The elements of the set of all outcomes of rolling two indistinguishable dice such that the numbers add to 6.

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Chapter 6.1, Problem 12E

Chapter 6.1, Problem 14E

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Chapter 6 Solutions

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The elements of the set of all outcomes of rolling two indistinguishable dice such that the numbers add to 6.

Solution Summary: The author explains that the set contains all outcomes of rolling two indistinguishable dice. Since the dice are distinguishable, the sample space for the toss of two dice is A=left1,2,3,4,5

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The elements of the set of all outcomes of rolling two indistinguishable dice such that the numbers add to 6.

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