Introductory Statistics (10th Edition)
Introductory Statistics (10th Edition)
10th Edition
ISBN: 9780321989178
Author: Neil A. Weiss
Publisher: PEARSON
bartleby

Concept explainers

Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear re…
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
bartleby

Videos

Textbook Question
Book Icon
Chapter 4.4, Problem 123E

In this exercise, you are asked to verify that the sum of the joint probabilities in a row or column of a joint probability distribution equals the marginal probability in that row or column. Consider the following joint probability distribution.

Chapter 4.4, Problem 123E, In this exercise, you are asked to verify that the sum of the joint probabilities in a row or column

  1. a. Explain why

R1 = ((R1 & C1) or   or (R1 & Cn )).

  1. b. Why are the events (R1 &C1), . . . , (R1 &Cn ) mutually exclusive?
  2. c. Explain why parts (a) and (b) imply that

P(R1) = P(R1 & C1)+· · ·+ P(R1 & Cn ).

This equation shows that the first row of joint probabilities sums to the marginal probability at the end of that row. A similar argument applies to any other row or column.

Expert Solution & Answer
Check Mark

Want to see the full answer?

Check out a sample textbook solution
Blurred answer
Previous
Chapter 4.4, Problem 122E
Next
Chapter 4.5, Problem 124E

Chapter 4 Solutions

Introductory Statistics (10th Edition)

Ch. 4.1 - Roughly speaking, what is an experiment? an event?Ch. 4.1 - Concerning the equal-likelihood model of...Ch. 4.1 - What is the difference between selecting a member...Ch. 4.1 - If a member is selected at random from a finite...Ch. 4.1 - An experiment has 20 possible outcomes, all...Ch. 4.1 - An experiment has 40 possible outcomes, all...Ch. 4.1 - State the frequentist interpretation of...Ch. 4.1 - Interpret each of the following probability...Ch. 4.1 - Interpret each of the following probability...Ch. 4.1 - Which of the following numbers could not possibly...
Ch. 4.1 - Which of the following numbers could not possibly...Ch. 4.1 - Oklahoma State Officials. Refer to Table 4.1 on...Ch. 4.1 - Oklahoma State Officials. Refer to Table 4.1 on...Ch. 4.1 - Playing Cards. An ordinary deck of playing cards...Ch. 4.1 - Poker Chips. A bowl contains 12 poker chips3 red,...Ch. 4.1 - In Exercises 4.164.26, express your probability...Ch. 4.1 - In Exercises 4.164.26, express your probability...Ch. 4.1 - In Exercises 4.164.26, express your probability...Ch. 4.1 - In Exercises 4.164.26, express your probability...Ch. 4.1 - In Exercises 4.164.26, express your probability...Ch. 4.1 - In Exercises 4.164.26, express your probability...Ch. 4.1 - In Exercises 4.164.26, express your probability...Ch. 4.1 - In Exercises 4.164.26, express your probability...Ch. 4.1 - In Exercises 4.164.26, express your probability...Ch. 4.1 - In Exercises 4.164.26, express your probability...Ch. 4.1 - In Exercises 4.164.26, express your probability...Ch. 4.1 - Housing Units. Refer to Exercise 4.19. a. Which,...Ch. 4.1 - Prob. 28ECh. 4.1 - The probability is 0.314 that the gestation period...Ch. 4.1 - The probability is 0.667 that the favorite in a...Ch. 4.1 - U.S. Governors. In 2013, according to the National...Ch. 4.1 - Prob. 33ECh. 4.1 - Bilingual and Trilingual. At a certain university...Ch. 4.1 - Consider the random experiment of tossing a coin...Ch. 4.1 - Roulette. An American roulette wheel contains 38...Ch. 4.1 - Cyber Affair. As found in USA TODAY, results of a...Ch. 4.1 - Belmont Stakes. The Belmont Stakes is the third...Ch. 4.1 - Prob. 39ECh. 4.1 - Lightning Casualties. An issue of Travel + Leisure...Ch. 4.2 - What type of graphical displays are useful for...Ch. 4.2 - Construct a Venn diagram representing the event a....Ch. 4.2 - Construct a Venn diagram representing the event a....Ch. 4.2 - Construct a Venn diagram representing the event a....Ch. 4.2 - Construct a Venn diagram representing the event a....Ch. 4.2 - Consider the set consisting of the first 12...Ch. 4.2 - Consider the set consisting of the first 10...Ch. 4.2 - What does it mean for two events to be mutually...Ch. 4.2 - Prob. 49ECh. 4.2 - Answer true or false to the following statement...Ch. 4.2 - Answer true or false to the following statement...Ch. 4.2 - Draw a Venn diagram portraying four mutually...Ch. 4.2 - Dice. When one die is rolled, the following six...Ch. 4.2 - Horse Racing. In a horse race, the odds against...Ch. 4.2 - Committee Selection. A committee consists of five...Ch. 4.2 - Prob. 56ECh. 4.2 - Prob. 57ECh. 4.2 - Horse Racing. Refer to Exercise 4.54. For each of...Ch. 4.2 - Prob. 59ECh. 4.2 - Prob. 60ECh. 4.2 - Diabetes Prevalence. In a report titled Behavioral...Ch. 4.2 - Family Planning. The following table provides a...Ch. 4.2 - World Series. The World Series in baseball is won...Ch. 4.2 - NBA Finals. The NBA Finals of basketball is played...Ch. 4.2 - Housing Units. The U.S. Census Bureau publishes...Ch. 4.2 - Protecting the Environment. A survey was conducted...Ch. 4.2 - Prob. 67ECh. 4.2 - Prob. 68ECh. 4.2 - Housing Units. Refer to Exercise 4.65. Among the...Ch. 4.2 - Prob. 70ECh. 4.2 - Die and Coin. Consider the following random...Ch. 4.2 - Jurors. From 10 men and 8 women in a pool of...Ch. 4.2 - Let A and B be events of a sample space. a....Ch. 4.2 - Prob. 74ECh. 4.2 - Suppose that A, B, and C are three events that...Ch. 4.2 - Let A, B, and C be events of a sample space....Ch. 4.3 - Playing Cards. An ordinary deck of playing cards...Ch. 4.3 - Prob. 78ECh. 4.3 - Suppose that A and B are mutually exclusive events...Ch. 4.3 - Suppose that C and D are mutually exclusive events...Ch. 4.3 - Let E be an event with probability 0.35. Find the...Ch. 4.3 - Let F be an event with probability 0.72. Find the...Ch. 4.3 - Prob. 83ECh. 4.3 - Prob. 84ECh. 4.3 - Suppose that A and B are events such that P(A) =...Ch. 4.3 - Suppose that A and B are events such that P(A) =...Ch. 4.3 - Prob. 87ECh. 4.3 - Sales Tax Receipts. The State of Texas maintains...Ch. 4.3 - Twelfth-Grade Smokers. The National Institute on...Ch. 4.3 - Oil Spills. The U.S. Coast Guard maintains a...Ch. 4.3 - Internet Access. From the document Computer and...Ch. 4.3 - Religion in America. According to the Religious...Ch. 4.3 - Ages of Senators. Refer to Exercise 4.87. Use the...Ch. 4.3 - Sales Tax Receipts. Refer to Exercise 4.88. Use...Ch. 4.3 - Student Debt. The Association of American...Ch. 4.3 - Naturalization. The U.S. Bureau of Citizenship and...Ch. 4.3 - Craps. In the game of craps, a player rolls two...Ch. 4.3 - Prob. 98ECh. 4.3 - School Enrollment. The National Center for...Ch. 4.3 - Suppose that A and B are mutually exclusive...Ch. 4.3 - Newspaper Subscription. A certain city has three...Ch. 4.3 - General Addition Rule Extended. The general...Ch. 4.4 - Identify three ways in which the total number of...Ch. 4.4 - Suppose that bivariate data are to be grouped into...Ch. 4.4 - Prob. 105ECh. 4.4 - Prob. 106ECh. 4.4 - In each of Exercises 4.1074.110, a. fill in the...Ch. 4.4 - In each of Exercises 4.1074.110, a. fill in the...Ch. 4.4 - In each of Exercises 4.1074.110, a. fill in the...Ch. 4.4 - In each of Exercises 4.1074.110, a. fill in the...Ch. 4.4 - Prob. 111ECh. 4.4 - Motor Vehicle Use. The Federal Highway...Ch. 4.4 - Prob. 113ECh. 4.4 - Farms. The U.S. Department of Agriculture...Ch. 4.4 - Field Trips. P. Li et al. analyzed existing...Ch. 4.4 - Prob. 116ECh. 4.4 - New England Patriots. Refer to Exercise 4.111. a....Ch. 4.4 - Motor Vehicle Use. Refer to Exercise 4.112. a. For...Ch. 4.4 - Prob. 119ECh. 4.4 - Farms. Refer to Exercise 4.114. A U.S. farm is...Ch. 4.4 - Prob. 121ECh. 4.4 - What does the general addition rule (Formula 4.3...Ch. 4.4 - In this exercise, you are asked to verify that the...Ch. 4.5 - Regarding conditional probability: a. What is it?...Ch. 4.5 - Give an example of the conditional probability of...Ch. 4.5 - Suppose that A and B are events such that P(A) =...Ch. 4.5 - Suppose that C and D are events such that P(C) =...Ch. 4.5 - Suppose that C and D are events such that P(C) =...Ch. 4.5 - Suppose that A and B are events such that P(A) =...Ch. 4.5 - In each of Exercises 4.1304.133, we have presented...Ch. 4.5 - In each of Exercises 4.1304.133, we have presented...Ch. 4.5 - In each of Exercises 4.1304.133, we have presented...Ch. 4.5 - In each of Exercises 4.1304.133, we have presented...Ch. 4.5 - Coin Tossing. A balanced dime is tossed twice. The...Ch. 4.5 - Playing Cards. One card is selected at random from...Ch. 4.5 - State Populations. From Infoplease, we obtained...Ch. 4.5 - Housing Units. The U.S. Census Bureau publishes...Ch. 4.5 - Protective Orders. In the article Judicial...Ch. 4.5 - New England Patriots. From the National Football...Ch. 4.5 - Acclaim or Attack. In the article A Functional...Ch. 4.5 - Self-Concept and Sightedness. Self-concept can be...Ch. 4.5 - Living Arrangements. As reported by the U.S....Ch. 4.5 - Smartphone Ownership. From the document Smartphone...Ch. 4.5 - HPV Vaccine. In the article Correlates for...Ch. 4.5 - Dentist Visits. The National Center for Health...Ch. 4.5 - Scientists and Engineers. The U.S. National...Ch. 4.5 - Property Crime. As reported by the Federal Bureau...Ch. 4.5 - Prob. 148ECh. 4.5 - Prob. 149ECh. 4.5 - Dice. Two balanced dice are thrown, one red and...Ch. 4.5 - Royal Offspring. A king and queen have two...Ch. 4.5 - New England Patriots. Refer to Exercise 4.139. a....Ch. 4.5 - Let A and B be events, each with positive...Ch. 4.5 - Drugs and Car Accidents. Suppose that it has been...Ch. 4.6 - Regarding the general multiplication rule and the...Ch. 4.6 - Suppose that A and B are two events. a. What does...Ch. 4.6 - Prob. 157ECh. 4.6 - Prob. 158ECh. 4.6 - Prob. 159ECh. 4.6 - Suppose P(A) = 7/8 and P(B | A) = 5/7. Find P(A...Ch. 4.6 - Prob. 161ECh. 4.6 - Prob. 162ECh. 4.6 - Prob. 163ECh. 4.6 - Prob. 164ECh. 4.6 - Prob. 165ECh. 4.6 - In each of Exercises 4.1654.176, decide whether or...Ch. 4.6 - In each of Exercises 4.1654.176, decide whether or...Ch. 4.6 - In each of Exercises 4.1654.176, decide whether or...Ch. 4.6 - Prob. 169ECh. 4.6 - Prob. 170ECh. 4.6 - Prob. 171ECh. 4.6 - Prob. 172ECh. 4.6 - Prob. 173ECh. 4.6 - Prob. 174ECh. 4.6 - Prob. 175ECh. 4.6 - Prob. 176ECh. 4.6 - Prob. 177ECh. 4.6 - Suppose that C, D, and E are independent events...Ch. 4.6 - Holiday Depression. According to the Opinion...Ch. 4.6 - Addiction Medicine. The report Addiction Medicine:...Ch. 4.6 - ESP Experiment. A person has agreed to participate...Ch. 4.6 - Cards. Cards numbered 1, 2, 3, . . . , 10 are...Ch. 4.6 - Class Levels. A frequency distribution for the...Ch. 4.6 - Governors. The National Governors Association...Ch. 4.6 - Medical School Faculty. The Association of...Ch. 4.6 - Injured Americans. The National Center for Health...Ch. 4.6 - U.S. Congress. The U.S. Congress, Joint Committee...Ch. 4.6 - Doctoral Degrees. The U.S. National Science...Ch. 4.6 - Coin Tossing. When a balanced dime is tossed three...Ch. 4.6 - Prob. 190ECh. 4.6 - Drawing Cards. Two cards are drawn at random from...Ch. 4.6 - Yahtzee. In the game of Yahtzee, five balanced...Ch. 4.6 - Prob. 193ECh. 4.6 - Prob. 194ECh. 4.6 - Traffic Fatalities. According to Accident Facts,...Ch. 4.6 - Death Penalty. One of the more contentious issues...Ch. 4.6 - Nuts and Bolts. A hardware manufacturer produces...Ch. 4.6 - Activity Limitations. The National Center for...Ch. 4.6 - Scholarships. Marilyn vos Savant writes the column...Ch. 4.6 - General Multiplication Rule Extended. For three...Ch. 4.6 - Prob. 201ECh. 4.6 - Calculus Pretest. Students are given three chances...Ch. 4.6 - In this exercise, you examine further the concepts...Ch. 4.6 - Prob. 204ECh. 4.6 - Prob. 205ECh. 4.6 - Coin Tossing. When a balanced coin is tossed four...Ch. 4.7 - What does it mean for four events to be...Ch. 4.7 - What does it mean for four events to be mutually...Ch. 4.7 - Are exhaustive events necessarily mutually...Ch. 4.7 - Explain why an event and its complement are always...Ch. 4.7 - In each of Exercises 4.2114.214, the events A1,...Ch. 4.7 - Prob. 212ECh. 4.7 - Prob. 213ECh. 4.7 - In each of Exercises 4.2114.214, the events A1,...Ch. 4.7 - Prob. 215ECh. 4.7 - Playing Golf. From the National Golf Foundation...Ch. 4.7 - Belief in Extraterrestrial Aliens. According to an...Ch. 4.7 - Prob. 218ECh. 4.7 - Education and Astrology. The following table...Ch. 4.7 - Chronic Illness and Participation. The aim of a...Ch. 4.7 - Obesity and Age. A person is said to be overweight...Ch. 4.7 - Corporations and Elections. Based on research by...Ch. 4.7 - Textbook Revision. Textbook publishers must...Ch. 4.7 - Broken Eggs. At a grocery store, eggs come in...Ch. 4.7 - Pap Tests. Medical tests are frequently used to...Ch. 4.7 - Monty Hall Problem. Several years ago, in a column...Ch. 4.7 - Red and Black. You have two cards. One is red on...Ch. 4.7 - Smoking and Lung Disease. Refer to Example 4.26 on...Ch. 4.8 - What are counting rules? Why are they important?Ch. 4.8 - Why is the basic counting rule (BCR) often...Ch. 4.8 - Prob. 231ECh. 4.8 - Identify the notation used for each of the...Ch. 4.8 - Prob. 233ECh. 4.8 - Prob. 234ECh. 4.8 - Prob. 235ECh. 4.8 - Prob. 236ECh. 4.8 - Determine the value of each quantity. a. 4P3 b....Ch. 4.8 - Determine the value of each quantity. a. 7P3 b....Ch. 4.8 - Prob. 239ECh. 4.8 - Determine the value of each quantity. a. 7C3 b....Ch. 4.8 - Prob. 241ECh. 4.8 - Prob. 242ECh. 4.8 - Prob. 243ECh. 4.8 - Home Models and Elevations. Refer to Example 4.27...Ch. 4.8 - Home Models and Elevations. Refer to Example 4.27...Ch. 4.8 - Prob. 246ECh. 4.8 - Zip Codes. The author spoke with a representative...Ch. 4.8 - Computerized Testing. A statistics professor needs...Ch. 4.8 - Telephone Numbers. In the United States, telephone...Ch. 4.8 - i Dolls. An advertisement for i Dolls states:...Ch. 4.8 - Prob. 251ECh. 4.8 - Testing for ESP. An extrasensory perception (ESP)...Ch. 4.8 - Los Angeles Dodgers. From the official website of...Ch. 4.8 - Prob. 254ECh. 4.8 - Assigning Sales Territories. The sales manager of...Ch. 4.8 - Five-Card Stud. A hand of five-card stud poker...Ch. 4.8 - IRS Audits. The Internal Revenue Service (IRS)...Ch. 4.8 - A Lottery. At a lottery, 100 tickets were sold and...Ch. 4.8 - Shake. Ten people attend a party. If each pair of...Ch. 4.8 - Championship Series. Professional sports leagues...Ch. 4.8 - Five-Card Draw. A hand of five-card draw poker...Ch. 4.8 - Senate Committees. The U.S. Senate consists of 100...Ch. 4.8 - Venus Throw. The Dr. Fishers Casebook feature...Ch. 4.8 - Prob. 264ECh. 4.8 - Quality Assurance. Refer to Example 4.36, which...Ch. 4.8 - The Birthday Problem. A biology class has 38...Ch. 4.8 - Mega Millions. Mega Millions is a multi-state...Ch. 4.8 - TrueFalse Tests. A student takes a truefalse test...Ch. 4.8 - Florida Battleground State. From the Washington...Ch. 4.8 - Sampling Without Replacement. A simple random...Ch. 4.8 - The Birthday Problem. Refer to Exercise 4.266, but...Ch. 4 - Why is probability theory important to statistics?Ch. 4 - Regarding the equal-likelihood model, a. what is...Ch. 4 - What meaning is given to the probability of an...Ch. 4 - Decide which of these numbers could not possibly...Ch. 4 - Identify a commonly used graphical technique for...Ch. 4 - What does it mean for two or more events to be...Ch. 4 - Suppose that E is an event. Use probability...Ch. 4 - Prob. 8RPCh. 4 - Identify one reason why the complementation rule...Ch. 4 - Prob. 10RPCh. 4 - The sum of the joint probabilities in a row or...Ch. 4 - Prob. 12RPCh. 4 - Prob. 13RPCh. 4 - Prob. 14RPCh. 4 - Prob. 15RPCh. 4 - State the basic counting rule (BCR).Ch. 4 - A, B, and C are mutually exclusive events such...Ch. 4 - Prob. 18RPCh. 4 - A and B are events such that P(A) = 0.2, P(B) =...Ch. 4 - Prob. 20RPCh. 4 - A and B are events such that P(A) = 0.4, P(B) =...Ch. 4 - Prob. 22RPCh. 4 - Prob. 23RPCh. 4 - A1, A2, and A3 are mutually exclusive and...Ch. 4 - Prob. 25RPCh. 4 - Prob. 26RPCh. 4 - How many samples of size 3 are possible from a...Ch. 4 - Prob. 28RPCh. 4 - TV Location. The Television Bureau of Advertising...Ch. 4 - Adjusted Gross Incomes. The Internal Revenue...Ch. 4 - Prob. 31RPCh. 4 - Prob. 32RPCh. 4 - Adjusted Gross Incomes. Refer to Problems 30 and...Ch. 4 - Adjusted Gross Incomes. Consider the events (not...Ch. 4 - School Enrollment. The National Center for...Ch. 4 - School Enrollment. Refer to the information given...Ch. 4 - School Enrollment. Refer to the information given...Ch. 4 - School Enrollment. Refer to the information given...Ch. 4 - Public Programs. During one year, the College of...Ch. 4 - Divorced Birds. Research by B. Hatchwell et al. on...Ch. 4 - Color Blindness. According to M. Neitz and J....Ch. 4 - Smartphone Ownership. The Pew Internet American...Ch. 4 - Quinella and Trifecta Wagering. In Example 4.31 on...Ch. 4 - Bridge. A bridge hand consists of an unordered...Ch. 4 - Sweet Sixteen. In the NCAA basketball tournament,...Ch. 4 - TVs and DVDs. According to Nielsen Media Research,...Ch. 4 - At the beginning of this chapter on pages 156157,...

Additional Math Textbook Solutions

Find more solutions based on key concepts
(a) Make a stem-and-leaf plot for these 24 observations on the number of customers who used a down-town CitiBan...

Applied Statistics in Business and Economics

1. Each of the following processes involves sampling from a population. Define the population, and state whethe...

Statistics for Engineers and Scientists

Provide an example of a qualitative variable and an example of a quantitative variable.

Elementary Statistics (Text Only)

To explain would this correlation increase, decrease or not change much if we remove the elephants.

Statistics Through Applications

Fill in the blank: The probability that a fair coin lands heads is 0.5. Therefore, we can be sure that if we to...

Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561

Empirical versus Theoretical A Monopoly player claims that the probability of getting a 4 when rolling a six-si...

Introductory Statistics (2nd Edition)

Knowledge Booster
Background pattern image
Statistics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Text book image
College Algebra
Algebra
ISBN:9781337282291
Author:Ron Larson
Publisher:Cengage Learning
Text book image
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Text book image
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Text book image
College Algebra
Algebra
ISBN:9781938168383
Author:Jay Abramson
Publisher:OpenStax
SEE MORE TEXTBOOKS
Mod-01 Lec-01 Discrete probability distributions (Part 1); Author: nptelhrd;https://www.youtube.com/watch?v=6x1pL9Yov1k;License: Standard YouTube License, CC-BY
Discrete Probability Distributions; Author: Learn Something;https://www.youtube.com/watch?v=m9U4UelWLFs;License: Standard YouTube License, CC-BY
Probability Distribution Functions (PMF, PDF, CDF); Author: zedstatistics;https://www.youtube.com/watch?v=YXLVjCKVP7U;License: Standard YouTube License, CC-BY
Discrete Distributions: Binomial, Poisson and Hypergeometric | Statistics for Data Science; Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=lHhyy4JMigg;License: Standard Youtube License