Elementary Statistics Books a la carte Plus NEW MyLab Statistics with Pearson eText - Access Card Package (6th Edition)
6th Edition
ISBN: 9780133876239
Author: Ron Larson, Betsy Farber
Publisher: PEARSON
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Chapter 3.1, Problem 36E
To determine
To obtain: The
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1- Let A = {A1, A2, ...), in which A, A, = 0, when i j.
a) Is A a π-system? If not, which element(s) should be added to A to become a π-system?
b) Prove that σ(A) consists of the finite or countable unions of elements of A; i.c., A E σ(A) if and
only if there exists finite or countable sequence {n} such that A = U₁An (Hint: Let F be such
class; prove that F is a σ-filed containing A.)
c) Let p ≥ 0 be a sequence of non-negative real numbers with Σip₁ = 1. Using p₁'s, how do you
construct a probability measure on σ(A)? (Hint: use extension theorem.)
2- Construct an example for which P(lim sup A,) = 1 and P(lim inf An) = 0.
In a town with 5000 adults, a sample of 50 is selected using SRSWOR and asked their opinion of a proposed municipal project; 30 are found to favor it and 20 oppose it. If, in fact, the adults of the town were equally divided on the proposal, what would be the probability of observing what has been observed? Approximate using the Binomial distribution. Compare this with the exact probability which is 0.0418.
Chapter 3 Solutions
Elementary Statistics Books a la carte Plus NEW MyLab Statistics with Pearson eText - Access Card Package (6th Edition)
Ch. 3.1 - Prob. 1TYCh. 3.1 - Prob. 2TYCh. 3.1 - Prob. 3TYCh. 3.1 - Prob. 4TYCh. 3.1 - Prob. 5TYCh. 3.1 - Prob. 6TYCh. 3.1 - Prob. 7TYCh. 3.1 - Prob. 8TYCh. 3.1 - Prob. 9TYCh. 3.1 - Prob. 10TY
Ch. 3.1 - Prob. 11TYCh. 3.1 - What is the difference between an outcome and an...Ch. 3.1 - Prob. 2ECh. 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 - Prob. 7ECh. 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 - Prob. 11ECh. 3.1 - Prob. 12ECh. 3.1 - Matching Probabilities In Exercises 1116, match...Ch. 3.1 - Matching Probabilities In Exercises 1116, match...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 - Prob. 19ECh. 3.1 - Identifying the Sample Space of a Probability...Ch. 3.1 - Prob. 21ECh. 3.1 - Prob. 22ECh. 3.1 - Prob. 23ECh. 3.1 - Prob. 24ECh. 3.1 - Prob. 25ECh. 3.1 - Prob. 26ECh. 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 - Prob. 35ECh. 3.1 - Prob. 36ECh. 3.1 - Prob. 37ECh. 3.1 - Prob. 38ECh. 3.1 - Prob. 39ECh. 3.1 - Prob. 40ECh. 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 - Prob. 44ECh. 3.1 - Classifying Types of Probability In Exercises...Ch. 3.1 - Classifying Types of Probability In Exercises...Ch. 3.1 - Prob. 47ECh. 3.1 - Prob. 48ECh. 3.1 - Prob. 49ECh. 3.1 - Prob. 50ECh. 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 - Prob. 55ECh. 3.1 - Prob. 56ECh. 3.1 - Prob. 57ECh. 3.1 - Prob. 58ECh. 3.1 - Prob. 59ECh. 3.1 - Prob. 60ECh. 3.1 - Prob. 61ECh. 3.1 - Prob. 62ECh. 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. 67ECh. 3.1 - Prob. 68ECh. 3.1 - Prob. 69ECh. 3.1 - Prob. 70ECh. 3.1 - Prob. 71ECh. 3.1 - Prob. 72ECh. 3.1 - Prob. 73ECh. 3.1 - Prob. 74ECh. 3.1 - Prob. 75ECh. 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 - Prob. 1TYCh. 3.2 - Prob. 2TYCh. 3.2 - Prob. 3TYCh. 3.2 - Prob. 4TYCh. 3.2 - Prob. 5TYCh. 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 - Prob. 7ECh. 3.2 - Prob. 8ECh. 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 - Prob. 16ECh. 3.2 - Prob. 17ECh. 3.2 - Prob. 18ECh. 3.2 - Prob. 19ECh. 3.2 - Using the Multiplication Rule In Exercises 1932,...Ch. 3.2 - Prob. 21ECh. 3.2 - Pickup Trucks In a survey, 510 U.S. adults were...Ch. 3.2 - Prob. 23ECh. 3.2 - Prob. 24ECh. 3.2 - Prob. 25ECh. 3.2 - Prob. 26ECh. 3.2 - Prob. 27ECh. 3.2 - Prob. 28ECh. 3.2 - Prob. 29ECh. 3.2 - Prob. 30ECh. 3.2 - Prob. 31ECh. 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 - 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 - Prob. 1TYCh. 3.3 - Prob. 2TYCh. 3.3 - Prob. 3TYCh. 3.3 - Prob. 4TYCh. 3.3 - Prob. 5TYCh. 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 - Prob. 9ECh. 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 - Prob. 19ECh. 3.3 - Prob. 20ECh. 3.3 - Prob. 21ECh. 3.3 - Prob. 22ECh. 3.3 - Prob. 23ECh. 3.3 - Prob. 24ECh. 3.3 - Prob. 25ECh. 3.3 - Eye Surrey The table shows the results of a survey...Ch. 3.3 - Writing Can two events with nonzero probabilities...Ch. 3.3 - In the Venn diagram shown at the left, P(A or B or...Ch. 3.3 - Prob. 29ECh. 3.3 - Prob. 30ECh. 3.3 - Run the simulation using each value of n one time....Ch. 3.3 - Prob. 2ACh. 3.3 - Prob. 1CSCh. 3.3 - Prob. 2CSCh. 3.3 - Prob. 3CSCh. 3.3 - Prob. 4CSCh. 3.3 - Prob. 5CSCh. 3.3 - Prob. 6CSCh. 3.4 - Prob. 1TYCh. 3.4 - Prob. 2TYCh. 3.4 - Prob. 3TYCh. 3.4 - Prob. 4TYCh. 3.4 - Prob. 5TYCh. 3.4 - Prob. 6TYCh. 3.4 - Prob. 7TYCh. 3.4 - Prob. 8TYCh. 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 - Prob. 8ECh. 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 - Prob. 13ECh. 3.4 - Prob. 14ECh. 3.4 - Prob. 15ECh. 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 - Prob. 27ECh. 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 - Prob. 32ECh. 3.4 - Prob. 33ECh. 3.4 - Lottery Number Selection A lottery has 52 numbers....Ch. 3.4 - Menu A restaurant offers a dinner special that...Ch. 3.4 - Prob. 36ECh. 3.4 - Water Pollution An environmental agency is...Ch. 3.4 - Prob. 38ECh. 3.4 - Prob. 39ECh. 3.4 - Prob. 40ECh. 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 - Prob. 49ECh. 3.4 - Prob. 50ECh. 3.4 - Prob. 51ECh. 3.4 - Prob. 52ECh. 3.4 - Prob. 53ECh. 3.4 - Prob. 54ECh. 3.4 - Defective Units A shipment of 10 microwave ovens...Ch. 3.4 - Prob. 56ECh. 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 - Prob. 1UACh. 3 - Prob. 2UACh. 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 - Prob. 3.1.11RECh. 3 - Prob. 3.1.12RECh. 3 - Prob. 3.1.13RECh. 3 - Prob. 3.1.14RECh. 3 - Telephone Numbers The telephone numbers for a...Ch. 3 - Telephone Numbers The telephone numbers for a...Ch. 3 - Prob. 3.2.17RECh. 3 - Prob. 3.2.18RECh. 3 - In Exercises 1922, determine whether the events...Ch. 3 - Prob. 3.2.20RECh. 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 - Prob. 3.3.27RECh. 3 - In Exercises 2932, find the probability. 39. You...Ch. 3 - A random sample of 250 working adults found that...Ch. 3 - Prob. 3.3.30RECh. 3 - Prob. 3.3.31RECh. 3 - In Exercises 2932, find the probability. 30. A...Ch. 3 - Prob. 3.3.33RECh. 3 - Prob. 3.3.34RECh. 3 - Prob. 3.3.35RECh. 3 - Prob. 3.3.36RECh. 3 - Prob. 3.3.37RECh. 3 - Prob. 3.3.38RECh. 3 - Prob. 3.3.39RECh. 3 - Prob. 3.3.40RECh. 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 - Prob. 3.4.52RECh. 3 - Prob. 3.4.53RECh. 3 - Take this quiz as you would take a quiz in class....Ch. 3 - Prob. 2CQCh. 3 - Prob. 3CQCh. 3 - Prob. 4CQCh. 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 - Prob. 4CTCh. 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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