Explanation Given Information: Two indistinguishable and two distinguishable dice are tossed. Formula used: The probability of an event E with sample space S is given by the formula, P ( E ) = n ( E ) n ( S ) . where n ( E ) represents a number of elements in set E and n ( S ) represents the number of elements in set S. Calculation: Consider the sample space when two indistinguishable dice are rolled, S = { ( 1 , 1 ) , ( 1 , 2 ) , ( 1 , 3 ) , ( 1 , 4 ) ( 1 , 5 ) ( 1 , 6 ) ( 2 , 2 ) , ( 2 , 3 ) , ( 2 , 4 ) ( 2 , 5 ) ( 2 , 6 ) ( 3 , 3 ) , ( 3 , 4 ) ( 3 , 5 ) ( 3 , 6 ) ( 4 , 4 ) ( 4 , 5 ) ( 4 , 6 ) , ( 5 , 5 ) , ( 5 , 6 ) ( 6 , 6 ) } The probability for the event { ( 4 , 4 ) , ( 2 , 3 ) } is given by the sum of the probabilities of ( 4 , 4 ) and ( 2 , 3 ) . The probability of the event ( 4 , 4 ) is: P ( 4 , 4 ) = 1 36 The probability of the event ( 2 , 3 ) is: P ( 2 , 3 ) = 1 12 The probability for the event { ( 4 , 4 ) , ( 2 , 3 ) } is: P ( ( 4 , 4 ) , ( 2 , 3 ) ) = 1 36 + 1 18 = 1 36 + 2 36 = 3 36 = 1 12 Consider the sample space when two distinguishable dice are rolled, S = { ( 1 , 1 ) , ( 1 , 2 ) , ( 1 , 3 ) , ( 1 , 4 ) , ( 1 , 5 ) , ( 1 , 6 ) ( 2 , 1 ) , ( 2 , 2 ) , ( 2 ,

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 8.3, Problem 19E

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To calculate: The probability of the event ${(4,4),(2,3)}$ when two indistinguishable dice are rolled and the corresponding event for a pair of distinguishable dice.

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Chapter 8.3, Problem 18E

Chapter 8.3, Problem 20E

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Chapter 8 Solutions

Finite Mathematics and Applied Calculus (MindTap Course List)

Ch. 8.1 - In Exercises 118, describe the sample space S of...Ch. 8.1 - Prob. 2E Ch. 8.1 - In Exercises 118, describe the sample space S of...Ch. 8.1 - Prob. 4E Ch. 8.1 - In Exercises 118, describe the sample space S of...Ch. 8.1 - Prob. 6E Ch. 8.1 - In Exercises 118, describe the sample space S of...Ch. 8.1 - Prob. 8E Ch. 8.1 - In Exercises 118, describe the sample space S of...Ch. 8.1 - Prob. 10E

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The probability of the event { ( 4 , 4 ) , ( 2 , 3 ) } when two indistinguishable dice are rolled and the corresponding event for a pair of distinguishable dice.

Solution Summary: The author calculates the probability of two indistinguishable and two distinguishable dice being rolled.

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To calculate: The probability of the event ${(4,4),(2,3)}$ when two indistinguishable dice are rolled and the corresponding event for a pair of distinguishable dice.

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Chapter 8 Solutions