Elementary Statistics: Picturing the World (7th Edition)
Elementary Statistics: Picturing the World (7th Edition)
7th Edition
ISBN: 9780134683416
Author: Ron Larson, Betsy Farber
Publisher: PEARSON
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Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba…
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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Chapter 3.4, Problem 21E

Security Code In how many ways can the letters A, B, C, D, E, and F be arranged for a six-letter security code?

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T1.4: Let ẞ(G) be the minimum size of a vertex cover, a(G) be the maximum size of an independent set and m(G) = |E(G)|. (i) Prove that if G is triangle free (no induced K3) then m(G) ≤ a(G)B(G). Hints - The neighborhood of a vertex in a triangle free graph must be independent; all edges have at least one end in a vertex cover. (ii) Show that all graphs of order n ≥ 3 and size m> [n2/4] contain a triangle. Hints - you may need to use either elementary calculus or the arithmetic-geometric mean inequality.
We consider the one-period model studied in class as an example. Namely, we assumethat the current stock price is S0 = 10. At time T, the stock has either moved up toSt = 12 (with probability p = 0.6) or down towards St = 8 (with probability 1−p = 0.4).We consider a call option on this stock with maturity T and strike price K = 10. Theinterest rate on the money market is zero.As in class, we assume that you, as a customer, are willing to buy the call option on100 shares of stock for $120. The investor, who sold you the option, can adopt one of thefollowing strategies:ˆ Strategy 1: (seen in class) Buy 50 shares of stock and borrow $380.ˆ Strategy 2: Buy 55 shares of stock and borrow $430.ˆ Strategy 3: Buy 60 shares of stock and borrow $480.ˆ Strategy 4: Buy 40 shares of stock and borrow $280.(a) For each of strategies 2-4, describe the value of the investor’s portfolio at time 0,and at time T for each possible movement of the stock.(b) For each of strategies 2-4, does the investor have…
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Chapter 3 Solutions

Elementary Statistics: Picturing the World (7th Edition)

Ch. 3.1 - For each probability experiment, determine the...Ch. 3.1 - You ask for a students age at his or her last...Ch. 3.1 - Prob. 3TYCh. 3.1 - How many license plates can you make when a...Ch. 3.1 - You select a card from a standard deck of playing...Ch. 3.1 - In Example 6, determine the probability that the...Ch. 3.1 - Find the probability that the next user surveyed...Ch. 3.1 - Based on previous counts, the probability of a...Ch. 3.1 - Use the frequency distribution in Example 7 to...Ch. 3.1 - Find the probability of tossing a tail and...
Ch. 3.1 - Your college identification number consists of...Ch. 3.1 - What is the difference between an outcome and an...Ch. 3.1 - Determine whether each number could represent the...Ch. 3.1 - Explain why the statement is incorrect: The...Ch. 3.1 - When you use the Fundamental Counting Principle,...Ch. 3.1 - Describe the law of large numbers in your own...Ch. 3.1 - List the three formulas that can be used to...Ch. 3.1 - True or False? In Exercises 710, determine whether...Ch. 3.1 - True or False? In Exercises 710, determine whether...Ch. 3.1 - A probability of 110 indicates an unusual event.Ch. 3.1 - True or False? In Exercises 710, determine whether...Ch. 3.1 - Matching Probabilities In Exercises 1116, match...Ch. 3.1 - Matching Probabilities In Exercises 1116, match...Ch. 3.1 - Matching Probabilities In Exercises 1116, match...Ch. 3.1 - Matching Probabilities In Exercises 1116, match...Ch. 3.1 - Matching Probabilities In Exercises 1116, match...Ch. 3.1 - Matching Probabilities In Exercises 1116, match...Ch. 3.1 - Finding the Probability of the Complement of an...Ch. 3.1 - Finding the Probability of the Complement of an...Ch. 3.1 - Finding the Probability of the Complement of an...Ch. 3.1 - Finding the Probability of the Complement of an...Ch. 3.1 - Finding the Probability of an Event In Exercises...Ch. 3.1 - Finding the Probability of an Event In Exercises...Ch. 3.1 - Finding the Probability of an Event In Exercises...Ch. 3.1 - Finding the Probability of an Event In Exercises...Ch. 3.1 - Identifying the Sample Space of a Probability...Ch. 3.1 - Identifying the Sample Space of a Probability...Ch. 3.1 - Identifying the Sample Space of a Probability...Ch. 3.1 - Identifying the Sample Space of a Probability...Ch. 3.1 - Identifying the Sample Space of a Probability...Ch. 3.1 - Identifying the Sample Space of a Probability...Ch. 3.1 - Identifying the Sample Space of a Probability...Ch. 3.1 - Identifying the Sample Space of a Probability...Ch. 3.1 - Identifying Simple Events In Exercises 3336,...Ch. 3.1 - Identifying Simple Events In Exercises 3336,...Ch. 3.1 - Identifying Simple Events In Exercises 3336,...Ch. 3.1 - Identifying Simple Events In Exercises 3336,...Ch. 3.1 - Using the Fundamental Counting Principle In...Ch. 3.1 - Using the Fundamental Counting Principle In...Ch. 3.1 - Using the Fundamental Counting Principle In...Ch. 3.1 - Using the Fundamental Counting Principle In...Ch. 3.1 - Finding Classical Probabilities In Exercises 4146,...Ch. 3.1 - Finding Classical Probabilities In Exercises 4146,...Ch. 3.1 - Finding Classical Probabilities In Exercises 4146,...Ch. 3.1 - Finding Classical Probabilities In Exercises 4146,...Ch. 3.1 - Finding Classical Probabilities In Exercises 4146,...Ch. 3.1 - Finding Classical Probabilities In Exercises 4146,...Ch. 3.1 - Finding Empirical Probabilities A polling...Ch. 3.1 - Finding Empirical Probabilities A polling...Ch. 3.1 - Using a Frequency Distribution to Find...Ch. 3.1 - Using a Frequency Distribution to Find...Ch. 3.1 - Using a Frequency Distribution to Find...Ch. 3.1 - Using a Frequency Distribution to Find...Ch. 3.1 - Classifying Types of Probability In Exercises...Ch. 3.1 - Classifying Types of Probability In Exercises...Ch. 3.1 - Classifying Types of Probability In Exercises...Ch. 3.1 - Classifying Types of Probability In Exercises...Ch. 3.1 - Classifying Types of Probability In Exercises...Ch. 3.1 - Classifying Types of Probability In Exercises...Ch. 3.1 - Finding the Probability of the Complement of an...Ch. 3.1 - Finding the Probability of the Complement of an...Ch. 3.1 - Finding the Probability of the Complement of an...Ch. 3.1 - Finding the Probability of the Complement of an...Ch. 3.1 - Using a Tree Diagram In Exercises 6366, a...Ch. 3.1 - Using a Tree Diagram In Exercises 6366, a...Ch. 3.1 - Using a Tree Diagram In Exercises 6366, a...Ch. 3.1 - Using a Tree Diagram In Exercises 6366, a...Ch. 3.1 - Access Code An access code consists of three...Ch. 3.1 - Access Code An access code consists of six...Ch. 3.1 - Wet or Dry? You are planning a three-day trip to...Ch. 3.1 - Wet or Dry? You are planning a three-day trip to...Ch. 3.1 - Prob. 71ECh. 3.1 - Wet or Dry? You are planning a three-day trip to...Ch. 3.1 - Graphical Analysis In Exercises 73 and 74, use the...Ch. 3.1 - Graphical Analysis In Exercises 73 and 74, use the...Ch. 3.1 - Using a Bar Graph to Find Probabilities In...Ch. 3.1 - Using a Bar Graph to Find Probabilities In...Ch. 3.1 - Using a Bar Graph to Find Probabilities In...Ch. 3.1 - Using a Bar Graph to Find Probabilities In...Ch. 3.1 - Prob. 79ECh. 3.1 - Prob. 80ECh. 3.1 - Prob. 81ECh. 3.1 - Prob. 82ECh. 3.1 - Using a Pie Chart to Find Probabilities In...Ch. 3.1 - Using a Pie Chart to Find Probabilities In...Ch. 3.1 - Prob. 85ECh. 3.1 - Using a Pie Chart to Find Probabilities In...Ch. 3.1 - College Football A stem-and-leaf plot for the...Ch. 3.1 - Individual Stock Price An individual stock is...Ch. 3.1 - Writing In Exercises 89 and 90, write a statement...Ch. 3.1 - Writing In Exercises 89 and 90, write a statement...Ch. 3.1 - Odds The chances of winning are often written in...Ch. 3.1 - Odds The chances of winning are often written in...Ch. 3.1 - Odds The chances of winning are often written in...Ch. 3.1 - Odds The chances of winning are often written in...Ch. 3.1 - Odds The chances of winning are often written in...Ch. 3.1 - Odds The chances of winning are often written in...Ch. 3.1 - Run the simulation using n = 1 without clicking...Ch. 3.1 - Run the applet to simulate the stock market...Ch. 3.2 - Refer to the survey in the second part of Example...Ch. 3.2 - Determine whether the events are independent or...Ch. 3.2 - 1. The probability that a salmon swims...Ch. 3.2 - The probability that a particular rotator cuff...Ch. 3.2 - In a jury selection pool, 65% of the people are...Ch. 3.2 - What is the difference between independent and...Ch. 3.2 - Give an example of (a) two events that are...Ch. 3.2 - What does the notation P(B|A) mean?Ch. 3.2 - Explain how to use the complement to find the...Ch. 3.2 - True or False? In Exercises 5 and 6, determine...Ch. 3.2 - True or False? In Exercises 5 and 6, determine...Ch. 3.2 - Finding Conditional Probabilities In Exercises 7...Ch. 3.2 - Finding Conditional Probabilities In Exercises 7...Ch. 3.2 - Classifying Events as Independent or Dependent In...Ch. 3.2 - Classifying Events as Independent or Dependent In...Ch. 3.2 - Classifying Events as Independent or Dependent In...Ch. 3.2 - Classifying Events as Independent or Dependent In...Ch. 3.2 - Classifying Events as Independent or Dependent In...Ch. 3.2 - Classifying Events as Independent or Dependent In...Ch. 3.2 - Classifying Events Based on Studies In Exercises...Ch. 3.2 - Classifying Events Based on Studies In Exercises...Ch. 3.2 - Classifying Events Based on Studies In Exercises...Ch. 3.2 - Classifying Events Based on Studies In Exercises...Ch. 3.2 - Using the Multiplication Rule In Exercises 1932,...Ch. 3.2 - Using the Multiplication Rule In Exercises 1932,...Ch. 3.2 - BRCA1 Gene Research has shown that approximately 1...Ch. 3.2 - Pickup Trucks In a survey, 510 U.S. adults were...Ch. 3.2 - Celebrities as Role Models In a sample of 1000...Ch. 3.2 - Knowing a Murder Victim In a sample of 1000 U.S....Ch. 3.2 - Best President In a sample of 1446 U.S. registered...Ch. 3.2 - Worst President In a sample of 1446 U.S....Ch. 3.2 - Blood Types The probability that an African...Ch. 3.2 - Blood Types The probability that a Caucasian...Ch. 3.2 - In Vitro Fertilization In a recent year, about...Ch. 3.2 - Lottery Tickets According to a survey, 49% of U.S....Ch. 3.2 - Digital Content in Schools According to a study,...Ch. 3.2 - Surviving Surgery A doctor gives a patient a 60%...Ch. 3.2 - According to Bayes Theorem, the probability of...Ch. 3.2 - According to Bayes Theorem, the probability of...Ch. 3.2 - According to Bayes Theorem, the probability of...Ch. 3.2 - According to Bayes Theorem, the probability of...Ch. 3.2 - According to Bayes Theorem, the probability of...Ch. 3.2 - Prob. 38ECh. 3.2 - Reliability of Testing A virus infects one in...Ch. 3.2 - Birthday Problem You are in a class that has 24...Ch. 3.2 - In Exercises 41 and 42, use the information below....Ch. 3.2 - In Exercises 41 and 42, use the information below....Ch. 3.3 - Determine whether the events are mutually...Ch. 3.3 - 1. A die is rolled. Find the probability of...Ch. 3.3 - Find the probability that the sales representative...Ch. 3.3 - 1. Find the probability that a donor selected at...Ch. 3.3 - Find the probability that a randomly selected...Ch. 3.3 - When two events are mutually exclusive, why is P(A...Ch. 3.3 - Give an example of (a) two events that are...Ch. 3.3 - True or False? In Exercises 36, determine whether...Ch. 3.3 - A die is rolled. Find the probability of rolling a...Ch. 3.3 - True or False? In Exercises 36, determine whether...Ch. 3.3 - True or False? In Exercises 36, determine whether...Ch. 3.3 - Graphical Analysis In Exercises 7 and 8, determine...Ch. 3.3 - Graphical Analysis In Exercises 7 and 8, determine...Ch. 3.3 - Recognizing Mutually Exclusive Events In Exercises...Ch. 3.3 - Recognizing Mutually Exclusive Events In Exercises...Ch. 3.3 - Recognizing Mutually Exclusive Events In Exercises...Ch. 3.3 - Recognizing Mutually Exclusive Events In Exercises...Ch. 3.3 - Students A physics class has 40 students. Of...Ch. 3.3 - Conference A teaching conference has an attendance...Ch. 3.3 - Carton Defects Of the cartons produced by a...Ch. 3.3 - Can Defects Of the cans produced by a company, 96%...Ch. 3.3 - Selecting a Card A card is selected at random from...Ch. 3.3 - Rolling a Die You roll a die. Find the probability...Ch. 3.3 - 19. U.S. Age Distribution The estimated percent...Ch. 3.3 - 20. Marijuana Use The percent of college students...Ch. 3.3 - Media Conduct The responses of 1254 voters to a...Ch. 3.3 - Brexit The responses of 1007 American adults to a...Ch. 3.3 - Business Degrees The table shows the numbers of...Ch. 3.3 - Education Tax The table shows the results of a...Ch. 3.3 - Charity The table shows the results of a survey...Ch. 3.3 - Eye Surrey The table shows the results of a survey...Ch. 3.3 - In the Venn diagram shown at the left, P(A or B or...Ch. 3.3 - Prob. 28ECh. 3.3 - Prob. 29ECh. 3.3 - Writing Can two events with nonzero probabilities...Ch. 3.3 - Run the simulation using each value of n one time....Ch. 3.3 - Prob. 2ACh. 3.3 - Find the probability that a randomly selected...Ch. 3.3 - Compare the probabilities from Exercise 1. 1. Find...Ch. 3.3 - A representative is selected at random. Find the...Ch. 3.3 - Among members of the House of Representatives, are...Ch. 3.3 - A senator is selected at random. Find the...Ch. 3.3 - Among members of the Senate, are the events being...Ch. 3.3 - Using the same row and column headings as the...Ch. 3.3 - A member of Congress is selected at random. Use...Ch. 3.4 - The Big 12 is a collegiate athletic conference...Ch. 3.4 - A psychologist shows a list of eight activities to...Ch. 3.4 - The board of directors of a company has 12...Ch. 3.4 - The contractor wants to plant six oak trees, nine...Ch. 3.4 - The manager of an accounting department wants to...Ch. 3.4 - A student advisory board consists of 20 members....Ch. 3.4 - Find the probability of being dealt 5 diamonds...Ch. 3.4 - A jury consists of five men and seven women. Three...Ch. 3.4 - Prob. 1ECh. 3.4 - When you calculate the number of combinations of r...Ch. 3.4 - Prob. 3ECh. 3.4 - True or False? In Exercises 36, determine whether...Ch. 3.4 - True or False? In Exercises 36, determine whether...Ch. 3.4 - True or False? In Exercises 36, determine whether...Ch. 3.4 - In Exercises 714, perform the indicated...Ch. 3.4 - In Exercises 714, perform the indicated...Ch. 3.4 - In Exercises 714, perform the indicated...Ch. 3.4 - In Exercises 714, perform the indicated...Ch. 3.4 - In Exercises 714, perform the indicated...Ch. 3.4 - Prob. 12ECh. 3.4 - In Exercises 714, perform the indicated...Ch. 3.4 - Prob. 14ECh. 3.4 - In Exercises 1518, determine whether the situation...Ch. 3.4 - In Exercises 1518, determine whether the situation...Ch. 3.4 - In Exercises 1518, determine whether the situation...Ch. 3.4 - In Exercises 1518, determine whether the situation...Ch. 3.4 - Video Games You have seven different video games....Ch. 3.4 - Skiing Eight people compete in a downhill ski...Ch. 3.4 - Security Code In how many ways can the letters A,...Ch. 3.4 - Starting Lineup The starting lineup for a softball...Ch. 3.4 - Footrace There are 50 runners in a race. How many...Ch. 3.4 - Singing Competition There are 16 finalists in a...Ch. 3.4 - Playlist A DJ is preparing a playlist of 24 songs....Ch. 3.4 - Archaeology Club An archaeology club has 38...Ch. 3.4 - Blood Donors At a blood drive, 8 donors with type...Ch. 3.4 - Necklaces You are putting 9 pieces of blue beach...Ch. 3.4 - Letters In how many distinguishable ways can the...Ch. 3.4 - Computer Science A byte is a sequence of eight...Ch. 3.4 - Experimental Group In order to conduct an...Ch. 3.4 - Jury Selection From a group of 36 people, a jury...Ch. 3.4 - Students A class has 40 students. In how many...Ch. 3.4 - Lottery Number Selection A lottery has 52 numbers....Ch. 3.4 - Menu A restaurant offers a dinner special that...Ch. 3.4 - Floral Arrangements A floral arrangement consists...Ch. 3.4 - Water Pollution An environmental agency is...Ch. 3.4 - Property Inspection A property inspector is...Ch. 3.4 - Senate Committee The U.S. Senate Committee on...Ch. 3.4 - University Committee The University of California...Ch. 3.4 - Horse Race A horse race has 12 entries. Assuming...Ch. 3.4 - Pizza Toppings A pizza shop offers nine toppings....Ch. 3.4 - Jukebox You look over the songs on a jukebox and...Ch. 3.4 - Officers The offices of president, vice president,...Ch. 3.4 - Food Allergies or Intolerances In Exercises 4548,...Ch. 3.4 - Food Allergies or Intolerances In Exercises 4548,...Ch. 3.4 - Food Allergies or Intolerances In Exercises 4548,...Ch. 3.4 - Food Allergies or Intolerances In Exercises 4548,...Ch. 3.4 - Lottery In a state lottery, you must correctly...Ch. 3.4 - Committee A company that has 200 employees chooses...Ch. 3.4 - Warehouse In Exercises 5154, a warehouse employs...Ch. 3.4 - Warehouse In Exercises 5154, a warehouse employs...Ch. 3.4 - Warehouse In Exercises 5154, a warehouse employs...Ch. 3.4 - Warehouse In Exercises 5154, a warehouse employs...Ch. 3.4 - Defective Units A shipment of 10 microwave ovens...Ch. 3.4 - Defective Disks A pack of 100 recordable DVDs...Ch. 3.4 - Employee Selection Four sales representatives for...Ch. 3.4 - Employee Selection Four sales representatives for...Ch. 3.4 - Cards In Exercises 5962, you are dealt a hand of...Ch. 3.4 - Cards In Exercises 5962, you are dealt a hand of...Ch. 3.4 - Prob. 61ECh. 3.4 - Cards In Exercises 5962, you are dealt a hand of...Ch. 3 - A Daily Number lottery has a three-digit number...Ch. 3 - A Daily Number lottery has a three-digit number...Ch. 3 - A Daily Number lottery has a three-digit number...Ch. 3 - In Exercises 14, identify the sample space of the...Ch. 3 - In Exercises 14, identify the sample space of the...Ch. 3 - In Exercises 14, identify the sample space of the...Ch. 3 - In Exercises 14, identify the sample space of the...Ch. 3 - In Exercises 5 and 6, use the Fundamental Counting...Ch. 3 - In Exercises 5 and 6, use the Fundamental Counting...Ch. 3 - In Exercises 712, classify the statement as an...Ch. 3 - In Exercises 712, classify the statement as an...Ch. 3 - In Exercises 712, classify the statement as an...Ch. 3 - In Exercises 712, classify the statement as an...Ch. 3 - In Exercises 712, classify the statement as an...Ch. 3 - In Exercises 712, classify the statement as an...Ch. 3 - In Exercises 13 and 14, use the table, which shows...Ch. 3 - In Exercises 13 and 14, use the table, which shows...Ch. 3 - Telephone Numbers The telephone numbers for a...Ch. 3 - Telephone Numbers The telephone numbers for a...Ch. 3 - In Exercises 17 and 18, use the table, which shows...Ch. 3 - In Exercises 17 and 18, use the table, which shows...Ch. 3 - In Exercises 1922, determine whether the events...Ch. 3 - In Exercises 1922, determine whether the events...Ch. 3 - Prob. 3.2.21RECh. 3 - Prob. 3.2.22RECh. 3 - Prob. 3.2.23RECh. 3 - Your sock drawer has 18 folded pairs of socks,...Ch. 3 - In Exercises 25 and 26, determine whether the...Ch. 3 - In Exercises 25 and 26, determine whether the...Ch. 3 - A random sample of 250 working adults found that...Ch. 3 - A sample of 6500 automobiles found that 1560 of...Ch. 3 - Prob. 3.3.29RECh. 3 - In Exercises 2932, find the probability. 30. A...Ch. 3 - Prob. 3.3.31RECh. 3 - Prob. 3.3.32RECh. 3 - In Exercises 33 and 34, use the pie chart at the...Ch. 3 - In Exercises 33 and 34, use the pie chart at the...Ch. 3 - In Exercises 3538, use the Pareto chart, which...Ch. 3 - In Exercises 3538, use the Pareto chart, which...Ch. 3 - In Exercises 3538, use the Pareto chart, which...Ch. 3 - In Exercises 3538, use the Pareto chart, which...Ch. 3 - In Exercises 2932, find the probability. 39. You...Ch. 3 - You are given that P(A or B) = 0.55 and P(A) +...Ch. 3 - Prob. 3.4.41RECh. 3 - Prob. 3.4.42RECh. 3 - Prob. 3.4.43RECh. 3 - Prob. 3.4.44RECh. 3 - Prob. 3.4.45RECh. 3 - Prob. 3.4.46RECh. 3 - Prob. 3.4.47RECh. 3 - Prob. 3.4.48RECh. 3 - In Exercises 4953, use counting principles to find...Ch. 3 - In Exercises 4953, use counting principles to find...Ch. 3 - A shipment of 200 calculators contains 3 defective...Ch. 3 - A class of 40 students takes a statistics exam....Ch. 3 - Prob. 3.4.53RECh. 3 - Take this quiz as you would take a quiz in class....Ch. 3 - The table shows the numbers (in thousands) of...Ch. 3 - The table shows the numbers (in thousands) of...Ch. 3 - Determine whether the events are mutually...Ch. 3 - From a pool of 30 candidates, the offices of...Ch. 3 - A shipment of 250 netbooks contains 3 defective...Ch. 3 - In Exercise 6. find the probability of the vending...Ch. 3 - Sixty-five runners compete in a 10k race. Your...Ch. 3 - A security code consists of a persons first and...Ch. 3 - Determine whether the events are mutually...Ch. 3 - The table shows the sixth, seventh, and eighth...Ch. 3 - The table shows the sixth, seventh, and eighth...Ch. 3 - A person is selected at random from the sample in...Ch. 3 - There are 16 students giving final presentations...Ch. 3 - You work in the security department of a banks...Ch. 3 - You work in the security department of a banks...Ch. 3 - You work in the security department of a banks...Ch. 3 - How many phrases did Mozart write to create the...Ch. 3 - How many possible variations are there in Mozarts...Ch. 3 - Prob. 3TCh. 3 - Use technology to randomly select two numbers from...
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