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Anh văn thương mại, kinh doanh PROBABILITY DEMYSTIFIEDDemystiﬁed SeriesAdvanced Statistics DemystiﬁedAlgebra DemystiﬁedAnatomy DemystiﬁedAstronomy DemystiﬁedBiology DemystiﬁedBusiness Statistics DemystiﬁedCalculus DemystiﬁedChemistry DemystiﬁedCollege Algebra DemystiﬁedDiﬀerential Equations DemystiﬁedDigital Electronics DemystiﬁedEarth Science DemystiﬁedElectricity DemystiﬁedElectronics DemystiﬁedEveryday Math DemystiﬁedGeometry DemystiﬁedMath Word Problems DemystiﬁedMicrobiology DemystiﬁedPhysics DemystiﬁedPhysiology DemystiﬁedPre-Algebra DemystiﬁedPrecalculus DemystiﬁedProbability DemystiﬁedProject Management DemystiﬁedRobotics DemystiﬁedStatistics DemystiﬁedTrigonometry DemystiﬁedPROBABILITY DEMYSTIFIEDALLAN **G.** BLUMANMcGRAW-HILLNew York Chicago San Francisco Lisbon LondonMadrid Mexico City Milan New Delhi San JuanSeoul Singapore Sydney TorontoCopyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved. Manufactured in the United States of America. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher. 0-07-146999-0 The material in this eBook also appears in the print version of this title: 0-07-144549-8. All trademarks are trademarks of their respective owners. Rather than put a trademark symbol after every occurrence of a trademarked name, we use names in an editorial fashion only, and to the benefit of the trademark owner, with no intention of infringement of the trademark. Where such designations appear in this book, they have been printed with initial caps. McGraw-Hill eBooks are available at special quantity discounts to use as premiums and sales promotions, or for use in corporate training programs. For more information, please contact George Hoare, Special Sales, at george_hoare@mcgraw-hill.com or (212) 904-4069. TERMS OF USE This is a copyrighted work and The McGraw-Hill Companies, Inc. (“McGraw-Hill”) and its licensors reserve all rights in and to the work. Use of this work is subject to these terms. Except as permitted under the Copyright Act of 1976 and the right to store and retrieve one copy of the work, you may not decompile, disassemble, reverse engineer, reproduce, modify, create derivative works based upon, transmit, distribute, disseminate, sell, publish or sublicense the work or any part of it without McGraw-Hill’s prior consent. You may use the work for your own noncommercial and personal use; any other use of the work is strictly prohibited. Your right to use the work may be terminated if you fail to comply with these terms. THE WORK IS PROVIDED “AS IS.” McGRAW-HILL AND ITS LICENSORS MAKE NO GUARANTEES OR WARRANTIES AS TO THE ACCURACY, ADEQUACY OR COMPLETENESS OF OR RESULTS TO BE OBTAINED FROM USING THE WORK, INCLUDING ANY INFORMATION THAT CAN BE ACCESSED THROUGH THE WORK VIA HYPERLINK OR OTHERWISE, AND EXPRESSLY DISCLAIM ANY WARRANTY, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. McGraw-Hill and its licensors do not warrant or guarantee that the functions contained in the work will meet your requirements or that its operation will be uninterrupted or error free. Neither McGraw-Hill nor its licensors shall be liable to you or anyone else for any inaccuracy, error or omission, regardless of cause, in the work or for any damages resulting therefrom. McGraw-Hill has no responsibility for the content of any information accessed through the work. Under no circumstances shall McGraw-Hill and/or its licensors be liable for any indirect, incidental, special, punitive, consequential or similar damages that result from the use of or inability to use the work, even if any of them has been advised of the possibility of such damages. This limitation of liability shall apply to any claim or cause whatsoever whether such claim or cause arises in contract, tort or otherwise. DOI: 10.1036/0071469990 Want to learn more?We hope you enjoy this McGraw-Hill eBook! If you’d like more information about this book, its author, or related books and websites, please click here.To all of my teachers, whose examples instilled in me my love ofmathematics and teaching.CONTENTSPreface ixAcknowledgments xiCHAPTER 1 Basic Concepts 1CHAPTER 2 Sample Spaces 22CHAPTER 3 The Addition Rules 43CHAPTER 4 The Multiplication Rules 56CHAPTER 5 Odds and Expectation 77CHAPTER 6 The Counting Rules 94CHAPTER 7 The Binomial Distribution 114CHAPTER 8 Other **Probability** Distributions 131CHAPTER 9 The Normal Distribution 147CHAPTER 10 Simulation 177CHAPTER 11 Game Theory 187CHAPTER 12 Actuarial Science 210Final Exam 229Answers to Quizzes and Final Exam 244Appendix: Bayes’ Theorem 249Index 255viiFor more information about this title, click herePREFACE‘‘The probable is what usually happens.’’ — AristotleProbability can be called the mathematics of chance. The theory of probabil-ity is unusual in the sense that we cannot predict with certainty the individualoutcome of a chance process such as ﬂipping a coin or rolling a die (singularfor dice), but we can assign a number that corresponds to the **probability** ofgetting a particular outcome. For example, the **probability** of getting a headwhen a coin is tossed is 1/2 and the **probability** of getting a two when a singlefair die is rolled is 1/6.We can also predict with a certain amount of accuracy that when a coin istossed a large number of times, the ratio of the number of heads to the totalnumber of times the coin is tossed will be close to 1/2.Probability theory is, of course, used in gambling. Actually, mathemati-cians began studying **probability** as a means to answer questions aboutgambling games. Besides gambling, **probability** theory is used in many otherareas such as insurance, investing, weather forecasting, genetics, and medicine,and in everyday life.What is this book about?First let me tell you what this book is not about:. This book is not a rigorous theoretical deductive mathematicalapproach to the concepts of **probability** This book is not a book on how to gamble.And most importantixCopyright © 2005 by The McGraw-Hill Companies, Inc. Click here for terms of use.. This book is not a book on how to win at gambling!This book presents the basic concepts of **probability** in a simple,straightforward, easy-to-understand way. It does require, however, aknowledge of arithmetic (fractions, decimals, and percents) and a knowledgeof basic algebra (formulas, exponents, order of operations, etc.). If you needa review of these concepts, you can consult another of my books in thisseries entitled Pre-Algebra Demystiﬁed.This book can be used to gain a knowledge of the basic concepts ofprobability theory, either as a self-study guide or as a supplementarytextbook for those who are taking a course in **probability** or a course instatistics that has a section on probability.The basic concepts of **probability** are explained in the ﬁrst two chapters.Then the addition and multiplication rules are explained. Followingthat, the concepts of odds and expectation are explained. The countingrules are explained in Chapter 6, and they are needed for the binomial andother **probability** distributions found in Chapters 7 and 8. The relationshipbetween **probability** and the normal distribution is presented in Chapter 9.Finally, a recent development, the Monte Carlo method of simulation, isexplained in Chapter 10. Chapter 11 explains how **probability** can be used ingame theory and Chapter 12 explains how **probability** is used in actuariawork centric world answers' title='chapter 1 living in a network centric world answers'>Chapter 11 explains how **probability** can be used ingame theory and Chapter 12 explains how **probability** is used in actuariarld theory pdf'>apter 1 living in a network centric world answers'>Chapter 11 explains how **probability** can be used ingame theory and Chapter 12 explains how **probability** is used in actuariarld powerpoint'>apter 1 living in a network centric world answers'>Chapter 11 explains how **probability** can be used ingame theory and Chapter 12 explains how **probability** is used in actuariaswers'>apter 1 living in a network centric world answers'>Chapter 11 explains how **probability** can be used ingame theory and Chapter 12 explains how **probability** is used in actuariammary'>apter 1 living in a network centric world answers'>Chapter 11 explains how **probability** can be used ingame theory and Chapter 12 explains how **probability** is used in actuarialscience. Special material on Bayes’ Theorem is presented in the Appendixbecause this concept is somewhat more diﬃcult than the other conceptspresented in this book.In addition to addressing the concepts of probability, each chapter endswith what is called a ‘‘Probability Sidelight.’’ These sections cover some ofthe historical aspects of the development of **probability** theory or somecommentary on how **probability** theory is used in gambling and everyday life.I have spent my entire career teaching mathematics at a level that moststudents can understand and appreciate. I have written this book with thesame objective in mind. Mathematical precision, in some cases, has beensacriﬁced in the interest of presenting **probability** theory in a simpliﬁed way.Good luck!Allan **G.** BlumanPREFACEx[...]... book.Summary Probability is the mathematics of chance. There are three typesof probability: classical probability, empirical probability, and subjective probability. Classical **probability** uses sample spaces. A sample space is theset of outcomes of a **probability** experiment. The range of **probability** is from0 to 1. If an event cannot occur, its **probability** is 0. If an event is certain tooccur, its probability. .. cards. The probability that the 7 of diamonds is selected is a. 113b.14c.152d.1268. A card is selected at random from a deck of 52 cards. The probability that it is a 7 is a. 14b.152c.752d.113CHAPTER 2 Sample Spaces38 CHAPTER QUIZ1. Which is not a type of probability? a. Classicalb. Empiricalc. Subjectived. Finite2. Rolling a die or tossing a coin is called a a. Sample experimentb.... called a a. Sample experimentb. **Probability** experimentc. Inﬁnite experimentd. Repeated experiment3. When an event cannot occur, its **probability** is a. 1b. 0c.12d. 0.014. The set of all possible outcomes of a **probability** experiment is called the a. Sample spaceb. Outcome spacec. Event spaced. Experimental space5. The range of the values a **probability** can assume is a. From 0 to 1b. From 1toỵ1c.... precision, in some cases, has beensacriﬁced in the interest of presenting **probability** theory in a simpliﬁed way.Good luck!Allan **G.** Bluman PREFACEx 3. When three coins are tossed, the **probability** of getting at least onetail is a. 38b.18c.78d.584. When three coins are tossed, the **probability** of getting two or moreheads is a. 38b.18c.12d.785. A box contains a penny, a nickel, a dime,... When a card is selected at random from a deck, ﬁnd the probability of getting a. A black card.b. A red queen.c. A heart or a spade.3. When a card is selected at random from a deck, ﬁnd the probability of getting a. A diamond or a face card.b. A club or an 8.c. A red card or a 6.4. When two dice are rolled, ﬁnd the **probability** of getting a. A sum of 7.b. A sum greater than 8.c. A sum less than... dice are rolled, ﬁnd the **probability** of getting a. A 5 on one or both dice.b. A sum greater than 12.c. A sum less than 13.CHAPTER 2 Sample Spaces33 9. A card is drawn from an ordinary deck of 52 cards. The probability that it is a spade is a. 14b.113c.152d.12610. A card is drawn from an ordinary deck of 52 cards. The probability that it is a 9 or a club is a. 1752b.58c.413d.3411.... selected at random from the word ‘‘Mississippi,’’ ﬁnd the probability that it is an ‘‘s.’’ a. 18b.12c.311d.41113. When a die is rolled, the **probability** of getting an 8 is a. 16b. 0c. 1d. 11214. In a survey of 180 people, 74 were over the age of 64. If a personis selected at random, what is the **probability** that the person isover 64? a. 1645b.3237c.3790d.539015. In a classroom... cards. The probability that it is a face card is a. 352b.14c.913d.313CHAPTER 2 Sample Spaces39 **probability** of the two outcomes when ﬂipping a coin. When the probability of an event is close to one, the event is almost sure to occur. For example,if the chance of it snowing tomorrow is 90%, more than likely, you’ll seesome snow. See Figure 1-1.Rule 2: When an event cannot occur, the probability. .. for any type of gambling game such as rolling dice, playingroulette, etc.Subjective Probability A third type of **probability** is called subjective probability. Subjective probability is based upon an educated guess, estimate, opinion, or inexactinformation. For example, a sports writer may say that there is a 30% probability that the Pittsburgh Steelers will be in the Super Bowl next year.Here the... chance of rain is 0.60 (60%), ﬁnd the **probability** that itwon’t rain.SOLUTION:Since P(E) = 0.60 and PEịẳ1 PEị, the **probability** that it won’t rain is1 À 0.60 = 0.40 or 40%. Hence the **probability** that it won’t rain is 40%.PRACTICE1. A box contains a $1 bill, a $2 bill, a $5 bill, a $10 bill, and a $20 bill.A person selects a bill at random. Find each probability: a. The bill selected is a $10 bill.b. . Actually, mathemati-cians began studying probability as a means to answer questions aboutgambling games. Besides gambling, probability theory is used in many. card at random, ﬁnd the probability thatthe card isa. The 4˘.b. A red card.c. A club.6. A ball is selected at random from a bag containing a red ball, ablue

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