Introduction to Probability and Statistics
14th Edition
ISBN: 9781133103752
Author: Mendenhall, William
Publisher: Cengage Learning
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Chapter 4.3, Problem 4.12E
a.
To determine
To list:the simple events
b.
To determine
To find: the probabilities that to assign each simple event.
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Twenty-eight applicants interested in working for the Food Stamp program took an examination designed
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Pam, Rob and Sam get a cake that is one-third chocolate, one-third vanilla, and one-third strawberry as shown below. They wish to fairly divide the cake using the lone chooser method. Pam likes strawberry twice as much as chocolate or vanilla. Rob only likes chocolate. Sam, the chooser, likes vanilla and strawberry twice as much as chocolate. In the first division, Pam cuts the strawberry piece off and lets Rob choose his favorite piece. Based on that, Rob chooses the chocolate and vanilla parts. Note: All cuts made to the cake shown below are vertical.Which is a second division that Rob would make of his share of the cake?
Three players (one divider and two choosers) are going to divide a cake fairly using the lone divider method. The divider cuts the cake into three slices (s1, s2, and s3).
If the choosers' declarations are Chooser 1: {s1 , s2} and Chooser 2: {s2 , s3}.
Using the lone-divider method, how many different fair divisions of this cake are possible?
Chapter 4 Solutions
Introduction to Probability and Statistics
Ch. 4.3 - Tossing a Die An experiment involves tossing a...Ch. 4.3 - Prob. 4.2ECh. 4.3 - A sample space contains 10 simple events:...Ch. 4.3 - Free Throws A particular basketball player hits...Ch. 4.3 - Four Coins A jar contains four coins: a nickel, a...Ch. 4.3 - Preschool or Not? On the first day of...Ch. 4.3 - Prob. 4.7ECh. 4.3 - The Urn Problem, continued Refer to Exercise 4.7....Ch. 4.3 - Need Eyeglasses? A survey classified a large...Ch. 4.3 - Prob. 4.10E
Ch. 4.3 - Jury Duty Three people are randomly selected to...Ch. 4.3 - Prob. 4.12ECh. 4.3 - Tea Tasters A food company plans to conduct an...Ch. 4.3 - -Meter Run Four equally qualified runners, John,...Ch. 4.3 - Fruit Flies In a genetics experiment, the...Ch. 4.3 - Prob. 4.16ECh. 4.4 - You have two groups of distinctly different items,...Ch. 4.4 - Prob. 4.18ECh. 4.4 - Prob. 4.19ECh. 4.4 - Combinations Evaluate these combinations: a. C35...Ch. 4.4 - Choosing People In how many ways can youselect...Ch. 4.4 - Choosing People, again In how many ways canyou...Ch. 4.4 - Prob. 4.23ECh. 4.4 - Coins Four coins are tossed. How many simple...Ch. 4.4 - The Urn Problem, again Three balls are...Ch. 4.4 - What to Wear? You own 4 pairs of jeans, 12...Ch. 4.4 - Itineraries A businessman in New York is...Ch. 4.4 - Vacation Plans Your family vacation involves...Ch. 4.4 - A Card Game Three students are playing a cardgame....Ch. 4.4 - Dinner at Gerard’s A French restaurant offers...Ch. 4.4 - Playing Poker Five cards are selected from...Ch. 4.4 - Prob. 4.32ECh. 4.4 - A Hospital Survey A study is to be conducted in...Ch. 4.4 - Traffic Problems Two city council members are tobe...Ch. 4.4 - Prob. 4.35ECh. 4.4 - Prob. 4.36ECh. 4.4 - Prob. 4.37ECh. 4.4 - Cramming A student prepares for an exam bystudying...Ch. 4.4 - Monkey Business A monkey is given 12 blocks:3...Ch. 4.6 - An experiment can result in one of five equally...Ch. 4.6 - Refer to Exercise 4.40. Use the definition of a...Ch. 4.6 - Refer to Exercise 4.40. Use the definition of...Ch. 4.6 - Refer to Exercise 4.40. Use the Addition and...Ch. 4.6 - Prob. 4.44ECh. 4.6 - Suppose P(A)=.1 and P(B)=.5 . a. If P(A|B)=.1 ,...Ch. 4.6 - Dice An experiment consists of tossing a single...Ch. 4.6 - Prob. 4.47ECh. 4.6 - Two fair dice are tossed. a. What is the...Ch. 4.6 - Suppose that P(A)=.4 and P(B)=.2 . If events A and...Ch. 4.6 - Prob. 4.50ECh. 4.6 - Suppose that P(A)=.4 and P(AB)=.12 . a. Find...Ch. 4.6 - Prob. 4.52ECh. 4.6 - Prob. 4.53ECh. 4.6 - Prob. 4.54ECh. 4.6 - Grant Funding Suppose a group of research...Ch. 4.6 - Drug Offenders A study of drug offenders who have...Ch. 4.6 - Prob. 4.57ECh. 4.6 - The Birthday Problem Two people enter a room and...Ch. 4.6 - Prob. 4.59ECh. 4.6 - Starbucks or Peet’s®? A college student frequents...Ch. 4.6 - Prob. 4.61ECh. 4.6 - Smoking and Cancer A survey of people in a...Ch. 4.6 - Smoke Detectors A smoke-detector system usestwo...Ch. 4.6 - Plant Genetics In 1865, Gregor Mendel suggesteda...Ch. 4.6 - Prob. 4.65ECh. 4.6 - Choosing a Mate Men and women often disagreeon how...Ch. 4.6 - Prob. 4.67ECh. 4.6 - Golfing Player A has entered a golf tournament but...Ch. 4.7 - Prob. 4.69ECh. 4.7 - Prob. 4.70ECh. 4.7 - Prob. 4.71ECh. 4.7 - Violent Crime City crime records show that 20%...Ch. 4.7 - Worker Error A worker-operated machine producesa...Ch. 4.7 - Airport Security Suppose that, in a particular...Ch. 4.7 - Football Strategies A particular football team is...Ch. 4.7 - No Pass, No Play Under the “no pass, no play”rule...Ch. 4.7 - Medical Diagnostics Different illnesses can...Ch. 4.7 - Cheating on Your Taxes? Suppose 5% of all...Ch. 4.7 - Screening Tests Suppose that a certain diseaseis...Ch. 4.8 - Discrete or Continuous? Identify the following as...Ch. 4.8 - Discrete or Continuous? II Identify the following...Ch. 4.8 - Probability Distribution I A random variable x has...Ch. 4.8 - Prob. 4.83ECh. 4.8 - Dice Let x equal the number observed on the throw...Ch. 4.8 - Grocery Visits Let x represent the number of times...Ch. 4.8 - If you toss a pair of dice, the sum T of the...Ch. 4.8 - RU Texting? The proportion of adults (18 years or...Ch. 4.8 - Which Key Fits? A key ring contains four office...Ch. 4.8 - Gender Bias? A company has five applicants for two...Ch. 4.8 - Defective Equipment A piece of electronic...Ch. 4.8 - Drilling Oil Wells Past experience has shown that,...Ch. 4.8 - Tennis, Anyone? Two tennis professionals, A and B,...Ch. 4.8 - Prob. 4.93ECh. 4.8 - Prob. 4.94ECh. 4.8 - Insuring Your Diamonds You can insure a $50,000...Ch. 4.8 - FDA Testing The maximum patent life for a new drug...Ch. 4.8 - Coffee Breaks Most coffee drinkers take a little...Ch. 4.8 - Prob. 4.98ECh. 4.8 - Actuaries A CEO is considering buying an insurance...Ch. 4 - Playing the Slots A slot machine has three slots;...Ch. 4 - Whistle Blowers Although there is legal...Ch. 4 - Prob. 4.102SECh. 4 - Refer to Exercise 4.102. By summing the...Ch. 4 - DVRs A retailer sells two styles of digital...Ch. 4 - Prob. 4.105SECh. 4 - Prob. 4.106SECh. 4 - Prob. 4.107SECh. 4 - Fire Alarms A fire-detection device uses three...Ch. 4 - Prob. 4.109SECh. 4 - Prob. 4.110SECh. 4 - Prob. 4.111SECh. 4 - Prob. 4.112SECh. 4 - Prob. 4.113SECh. 4 - Prob. 4.114SECh. 4 - Prob. 4.115SECh. 4 - Prob. 4.116SECh. 4 - Prob. 4.117SECh. 4 - Prob. 4.118SECh. 4 - Prob. 4.119SECh. 4 - Prob. 4.120SECh. 4 - Prob. 4.121SECh. 4 - Contract Negotiations Experience has shown...Ch. 4 - Prob. 4.123SECh. 4 - Prob. 4.124SECh. 4 - Prob. 4.125SECh. 4 - Prob. 4.126SECh. 4 - Mass Transit Only 40% of all people in a...Ch. 4 - Prob. 4.128SECh. 4 - Prob. 4.129SECh. 4 - Prob. 4.130SECh. 4 - Flextime A survey to determine the availability of...Ch. 4 - Prob. 4.132SECh. 4 - Pepsi™ or Coke™? A taste-testing experiment is...Ch. 4 - Viruses A certain virus afflicted the families in...Ch. 4 - Prob. 4.135SECh. 4 - Independence and Mutually Exclusive Suppose that...Ch. 4 - Prob. 4.137SE
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