Explanation Calculation: Define the variables: r : Red ball g : Green ball w : White ball The set of all the possible outcomes in an experiment is termed as sample space. In the given situation, there are three red balls, two green balls and one white ball. This indicates that the red ball “ r ” can be occurred at most three times, the green ball “ g ” can be occurred at most two times and the white ball can be occurred one time and it cannot be repeated. Therefore, the sample space for the given experiment is Ω = { r r r , r r g , r r w , r w g , r g w , r g r , r w r , r g g , g g r , g g w , g r r , g r w , g w r , g r g , g w g , w r r , w g g , w r g , w g r } . Answer will vary. One of the possible answers is given below: The event is defined as follows: Event A : At least two red balls Event B : At least one green balls Event C : First ball is white The elements of the event “ A = At least two red balls” is calculated as follows: From the sample space, it can be observed that the event of getting “at least two red balls” is A = { r r r , r r g , r r w , r g r , r w r , g r r , w r r } . The elements of the event “ B = At least one green balls” is calculated as follows: From the sample space, it can be observed that the event of getting “at least one green balls” is B = { r r g , r w g , r g w , r g r , r g g , g g r , g g w , g r r , g r w , g w r , g r g , g w g , w g g , w r g , w g r } . The elements of the event “ C = First ball is white” is calculated as follows: From the sample space, it can be observed that the event of getting “first ball is white” is C = { w r r , w g g , w r g , w g r } . The elements of the event A ∩ B is obtained as follows: Intersection of A and B : The set of all elements that belong to both A and B. The common elements of the events A and B is { r r g , r g r , g r r } . Therefore, the elements of the event A ∩ B is, A ∩ B = { r r g , r g r , g r r }

Mathematical Statistics and Data Analysis

3rd Edition

ISBN: 9781111793715

Author: John A. Rice

Publisher: Cengage Learning

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Chapter 1.8, Problem 3P

To determine

List the sample space for the given experiment.

Define the events A, B and C and also find their unions and intersections.

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Chapter 1 Solutions

Mathematical Statistics and Data Analysis

Ch. 1.8 - Prob. 1P Ch. 1.8 - Prob. 2P Ch. 1.8 - Prob. 3P Ch. 1.8 - Prob. 4P Ch. 1.8 - Prob. 5P Ch. 1.8 - Prob. 6P Ch. 1.8 - Prob. 7P Ch. 1.8 - Prob. 8P Ch. 1.8 - Prob. 9P Ch. 1.8 - Prob. 10P

Ch. 1.8 - Prob. 11P Ch. 1.8 - Prob. 12P Ch. 1.8 - Prob. 13P Ch. 1.8 - Prob. 14P Ch. 1.8 - Prob. 15P Ch. 1.8 - Prob. 16P Ch. 1.8 - Prob. 17P Ch. 1.8 - Prob. 18P Ch. 1.8 - Prob. 19P Ch. 1.8 - Prob. 20P Ch. 1.8 - Prob. 21P Ch. 1.8 - Prob. 22P Ch. 1.8 - Prob. 23P Ch. 1.8 - Prob. 24P Ch. 1.8 - Prob. 25P Ch. 1.8 - Prob. 26P Ch. 1.8 - Prob. 27P Ch. 1.8 - Prob. 28P Ch. 1.8 - Prob. 29P Ch. 1.8 - Prob. 30P Ch. 1.8 - Prob. 31P Ch. 1.8 - Prob. 32P Ch. 1.8 - Prob. 33P Ch. 1.8 - Prob. 34P Ch. 1.8 - Prob. 35P Ch. 1.8 - Prob. 36P Ch. 1.8 - Prob. 37P Ch. 1.8 - Prob. 38P Ch. 1.8 - Prob. 39P Ch. 1.8 - Prob. 40P Ch. 1.8 - Prob. 41P Ch. 1.8 - Prob. 42P Ch. 1.8 - Prob. 43P Ch. 1.8 - Prob. 44P Ch. 1.8 - Prob. 45P Ch. 1.8 - Prob. 46P Ch. 1.8 - Prob. 47P Ch. 1.8 - Prob. 48P Ch. 1.8 - Prob. 49P Ch. 1.8 - Prob. 50P Ch. 1.8 - Prob. 51P Ch. 1.8 - Prob. 52P Ch. 1.8 - Prob. 53P Ch. 1.8 - Prob. 54P Ch. 1.8 - Prob. 55P Ch. 1.8 - Prob. 56P Ch. 1.8 - Prob. 57P Ch. 1.8 - Prob. 59P Ch. 1.8 - Prob. 60P Ch. 1.8 - Prob. 61P Ch. 1.8 - Prob. 62P Ch. 1.8 - Prob. 63P Ch. 1.8 - Prob. 64P Ch. 1.8 - Prob. 65P Ch. 1.8 - Prob. 66P Ch. 1.8 - Prob. 67P Ch. 1.8 - Prob. 68P Ch. 1.8 - Prob. 69P Ch. 1.8 - Prob. 70P Ch. 1.8 - Prob. 71P Ch. 1.8 - Prob. 72P Ch. 1.8 - Prob. 73P Ch. 1.8 - Prob. 74P Ch. 1.8 - Prob. 75P Ch. 1.8 - Prob. 77P Ch. 1.8 - Prob. 78P Ch. 1.8 - Prob. 79P Ch. 1.8 - Prob. 80P

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List the sample space for the given experiment. Define the events A , B and C and also find their unions and intersections.

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List the sample space for the given experiment. Define the events A, B and C and also find their unions and intersections.

Chapter 1 Solutions

List the sample space for the given experiment.

Define the events A, B and C and also find their unions and intersections.