The Heart of Mathematics: An Invitation to Effective Thinking
4th Edition
ISBN: 9781118156599
Author: Edward B. Burger, Michael Starbird
Publisher: Wiley, John & Sons, Incorporated
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 10.4, Problem 2MS
Electoral college. Briefly outline a voting scheme used in the United States where an election between two candidates can be held and the winner is not the person having the most popular votes. Give a specific example where this paradoxical situation occurred.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
please help me with this question ASAP
Problem: The Gerber County Paintball League has just completed its10th season. Help the league secretary finalize this year's standings by matching each team to its color, and final ranking.i. The "Night Ninjas" was ranked 1 place ahead of the green team.ii. The group that finished first is either the "Night Ninjas" or the purple team.iii. The "Splat Squad" finished first.iv. The white team was ranked somewhere behind the "Color Blinds".v. The "Color Blinds" finished third.
What are the final ranks of Color Blind, Night ninjas, Splat squad, Target bomb?What are the corresponding color for the team Color Blind, Night ninjas, Splat squad, Target bomb?
Example 7. In a survey of 35 students, 17 have opted Management, 10 have
opted Management, but not Engineering. Find the number of Students who have
opted both Management and Engineering and the number of students who have
opted Engineering but not Management, if it is given that each student has opted
either Management or Engineering or both.
Chapter 10 Solutions
The Heart of Mathematics: An Invitation to Effective Thinking
Ch. 10.1 - What do you expect? How do you compute an expected...Ch. 10.1 - The average bite. Your little sister loves visits...Ch. 10.1 - A tooth for a tooth? Suppose your cousins Tooth...Ch. 10.1 - Spinning wheel. Suppose the spinner shown is...Ch. 10.1 - Fair game. What does it mean for a game to be...Ch. 10.1 - Cross on the green (S). A standard roulette wheel...Ch. 10.1 - In the red. Given the bet from Mindscape 6, what...Ch. 10.1 - Free Lotto. For several years in Massachusetts,...Ch. 10.1 - Bank value. What is the expected value of keeping...Ch. 10.1 - Value of money. In Newcombs Paradox, first suppose...
Ch. 10.1 - Die roll. What is the expected value of each of...Ch. 10.1 - Dice roll (ExH). What is the expected value of...Ch. 10.1 - Fair is foul. Someone has a weighted coin that...Ch. 10.1 - Foul is fair (S). Someone has a weighted coin that...Ch. 10.1 - Cycle cycle (H). You live in an area where the...Ch. 10.1 - Whats your pleasure? You have three options for...Ch. 10.1 - Roulette expectation. A standard roulette wheel...Ch. 10.1 - Fair wheeling. You are at the roulette table and...Ch. 10.1 - High rolling (H). Here is a die game you play...Ch. 10.1 - Fair rolling. Suppose you are considering the game...Ch. 10.1 - Spinning wheel. You pay $5, pick one of the four...Ch. 10.1 - Dice (ExH). You place a bet and then roll two fair...Ch. 10.1 - Uncoverable bases. Show by a specific example how...Ch. 10.1 - Under the cap. A national soda company runs a...Ch. 10.1 - Two coins in a fountain. You pay Si for two coins...Ch. 10.1 - Three coins in a fountain. You pay $5 for three...Ch. 10.1 - Insure (S). You own a $9000 car and a $850...Ch. 10.1 - Get a job (H). You search for a job. Three...Ch. 10.1 - Take this job and... Given the employment scenario...Ch. 10.1 - Book value. Refer back to our analysis of the...Ch. 10.1 - In search of... A group of deep-sea divers...Ch. 10.1 - Solid gold. There is a 50% chance that the price...Ch. 10.1 - Four out of five. In Newcombs Paradox, suppose...Ch. 10.1 - Chevalier de Méré. Suppose that the Chevalier de...Ch. 10.1 - The St. Petersburg paradox. Here is an interesting...Ch. 10.1 - Coin or god. In Newcombs Paradox, first suppose...Ch. 10.1 - An investment. You wish to invest $1000, and you...Ch. 10.1 - Pap test (H). Assume that the insurance value of a...Ch. 10.1 - Prob. 40MSCh. 10.1 - Spin to win. To play a certain carnival game, you...Ch. 10.1 - Spinner winner. To play a different carnival game,...Ch. 10.1 - Insurance wagering (H). From the point of view of...Ch. 10.1 - Probable cause. Continuing the scenario from the...Ch. 10.1 - The bicycle thief. Some entrepreneurial classmates...Ch. 10.2 - Remarkably risky. List two activities that are...Ch. 10.2 - Surprisinly safe. List two activities that are...Ch. 10.2 - Infectious numbers (H). Suppose a disease is...Ch. 10.2 - SARS scars (S). Suppose a new vaccine that...Ch. 10.2 - A hairy pot. At a certain famous school of...Ch. 10.2 - Blonde, bleached blonde (H). You have high...Ch. 10.2 - Blonde again (S). Given the scenario in Mindscape...Ch. 10.2 - Bleached again. Given the scenario in Mindscape 6,...Ch. 10.2 - Safety first. Suppose a particular car is widely...Ch. 10.2 - Scholarship winner (ExH). You apply for a national...Ch. 10.2 - Less safe (ExH). Given the scenario in our air...Ch. 10.2 - Aw, nuts! Suppose that the loss of life expectancy...Ch. 10.2 - Dont cell! (H) Suppose you are a U.S. senator and...Ch. 10.2 - Buy low and cell high (H). The microwaves produced...Ch. 10.2 - Taxi blues (H). An eyewitness observes a...Ch. 10.2 - More taxi blues (S). An eyewitness observes a...Ch. 10.2 - Few blues. An eyewitness observes a hit-and-run...Ch. 10.2 - More safety. Given the scenario of our earlier air...Ch. 10.2 - Reduced safety. Given the scenario of our air...Ch. 10.2 - HIV tests. Recall that, in the United States,...Ch. 10.2 - More HIV tests. Given the tests described in the...Ch. 10.2 - Super sale. The bookstore is having a super sale...Ch. 10.2 - V.isk risk (H). You always sort your laundry into...Ch. 10.2 - Bag for life. An insurance company estimates that...Ch. 10.2 - Mooving sale. Plush toy versions of your college...Ch. 10.2 - Reweighing life expectancy An example in this...Ch. 10.3 - Simple interest (H). Suppose you deposit $500 into...Ch. 10.3 - Less simple interest. Suppose that at the...Ch. 10.3 - The power of powers (H). In this section we...Ch. 10.3 - Crafty compounding. Two thousand years ago, a...Ch. 10.3 - Keg costs. List some of the opportunity costs...Ch. 10.3 - You can bank on us (or them) (S). You wish to...Ch. 10.3 - The Kennedy compound. You wish to ivest $1000 for...Ch. 10.3 - Three times a lady. The Three-Timesa-Year Savings...Ch. 10.3 - Baker kneads dough (ExH). Your favorite baker,...Ch. 10.3 - I want my ATV! You want to purchase a cool, yellow...Ch. 10.3 - Lottery loot later? You have a big problem: Youve...Ch. 10.3 - Open sesame (S). Bert and Ernie each open a...Ch. 10.3 - Jelly-filled investments (H). Suppose you purchase...Ch. 10.3 - Taking stock. Suppose that a stock transaction...Ch. 10.3 - Making your pocketbook stocky. Suppose that a...Ch. 10.3 - Money-tree house. You decide you wish to build...Ch. 10.3 - Future vlaue (S). What is the future value of $...Ch. 10.3 - Present value (ExH). On the first day of your...Ch. 10.3 - Double or nothing (H). You decide you wish to...Ch. 10.3 - Triple or nothing. You decide you wish to triple...Ch. 10.3 - Power versus product (S). In this section we...Ch. 10.3 - Double vision. Suppose we have $P and we invest it...Ch. 10.3 - Adding up the bucks (H). You have a job every...Ch. 10.3 - Fiddling for dollars. As presented in the section...Ch. 10.3 - Facebank. Your roommates are developing some...Ch. 10.3 - Boatload o cash. At age 12 you dream of sailing...Ch. 10.3 - Houseload o cash. You want to buy a house by age...Ch. 10.4 - Landslide Lyndon. The two candidates in the 1948...Ch. 10.4 - Electoral college. Briefly outline a voting scheme...Ch. 10.4 - Voting for voting. What are some differences...Ch. 10.4 - Voting for sport. Given an example (ideally from...Ch. 10.4 - The point of the arrow (S). What does Arrows...Ch. 10.4 - Dictating an election through a dictator. Suppose...Ch. 10.4 - Pro- or Con-dorcet? (S) Consider the following...Ch. 10.4 - Where is Dr. Pepper? (S) Given the voting data...Ch. 10.4 - Approval drinking (H). Returning to the voting...Ch. 10.4 - Mindscapes 10 through 15 are based on the...Ch. 10.4 - Mindscapes 10 through 15 are based on the...Ch. 10.4 - Mindscapes 10 through 15 are based on the...Ch. 10.4 - Mindscapes 10 through 15 are based on the...Ch. 10.4 - Mindscapes 10 through 15 are based on the...Ch. 10.4 - Mindscapes 10 through 15 are based on the...Ch. 10.4 - Whats it all about, Ralphie? Many people believe...Ch. 10.4 - Two, too (ExH). Given an election between just two...Ch. 10.4 - Two, too II (ExH). Given an election between just...Ch. 10.4 - Instant runoffs. One way to avoid the lengthy...Ch. 10.4 - Run runoff. Given the method of instant runoff...Ch. 10.4 - Coin coupling. For this challenge, you will need...Ch. 10.4 - From money-mating to cupids arrow. Explain how the...Ch. 10.4 - Vote night. There are four candidates running for...Ch. 10.4 - Wroof recount. The election in the previous...Ch. 10.4 - Biggest loser? Who was the biggest loser in the...Ch. 10.4 - The X-act winner. Your schools math club has 73...Ch. 10.4 - Borda rules. Candidates A, B, and C are running...Ch. 10.5 - Prob. 1MSCh. 10.5 - Understanding icing (S). Suppose a person who had...Ch. 10.5 - Liquid gold. Suppose you and your two brothers are...Ch. 10.5 - East means West. Suppose you have a triangular...Ch. 10.5 - Two-bedroom bliss (H). Suppose you and a roommate...Ch. 10.5 - Your preference. Suppose the accompanying figure...Ch. 10.5 - Bulk. Suppose for you, bigger is better, so your...Ch. 10.5 - Dont move that knif. Give a specific scenario to...Ch. 10.5 - Prob. 9MSCh. 10.5 - Just do it. Get three people together and have...Ch. 10.5 - The real world. Give three real-world examples...Ch. 10.5 - Same tastes (H). If you are dividing a cake among...Ch. 10.5 - Crossing the line. In each triangle shown on the...Ch. 10.5 - Cutting up Mass (S). You, Joan, and John want to...Ch. 10.5 - Where to cut (H). The accompanying figure pictures...Ch. 10.5 - Land preference (ExH). Suppose you are preparing...Ch. 10.5 - Uneven pair (S). Suppose two people want to divide...Ch. 10.5 - Diversity pays. Explain why having differences of...Ch. 10.5 - Be fair. The moving-knife and yelling Stop method...Ch. 10.5 - Nuclear dump (ExH). Suppose there is a nuclear...Ch. 10.5 - Disarming (H). Two nuclear superpowers decide to...Ch. 10.5 - Cupcakes. Suppose you had 100 different cupcakes...Ch. 10.5 - Barely consistent. It is possible for Chris to...Ch. 10.5 - Your X. You and your ex-roommate happen to share a...Ch. 10.5 - Musical Xs. You play the violin in a chamber trio...Ch. 10.5 - Cake plot. Imagine a cake in the shape of a...Ch. 10.5 - Cake trisection. Imagine a cake in the shape of a...Ch. 10.5 - Roomate wrangling. You and a friend rent a...
Additional Math Textbook Solutions
Find more solutions based on key concepts
The feasible set for the nutrition problem of Example 1 is shown in Fig. 12. The cost 21x+14y. Without using th...
Finite Mathematics & Its Applications (12th Edition)
a. Fill in the missing numbers in the following factor tree. b. How could you find the top numbers without find...
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
In the following exercises, vectors u and v are given. Find unit vector w in the direction of the cross product...
Calculus Volume 3
Challenge Yourself In Example 6, we found that the average daily balance method gave the highest finance charge...
Mathematics All Around (6th Edition)
Let 2n (equally spaced) points on a circle be chosen. Show that the number of ways to join these points in pair...
Introductory Combinatorics
CHECK POINT I You deposit $3000 in s savings account at Yourtown Bank, which has rate of 5%. Find the interest ...
Thinking Mathematically (7th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- A poll of students showed that 45 percent liked basketball, 50 percent liked soccer, 40 percent liked football, 20 percent liked both basketball and soccer, 20 percent liked both soccer and football, 25 percent liked both basketball and football, and 10 percent liked all three sports. What percentage of students like only one sport? What percentage does not like any of the three sports? percent of students like only one sport. percent of students do not like any of the three sports.arrow_forwardProblem: The Gerber County Paintball League has just completed its 10th season. Help the league secretary finalize this year's standings by matching each team to its color, and final ranking.i. The "Night Ninjas" was ranked 1 place ahead of the green team.ii. The group that finished first is either the "Night Ninjas" or the purple team. iii. The "Splat Squad" finished first.iv. The white team was ranked somewhere behind the "Color Blinds".v. The "Color Blinds" finished third. Which is the first, second, third, and fourth in rank? What is the corresponding color of each team?arrow_forwardSally is interested in finding out if the political party affiliation of Americans who are registered to vote is related to whether or not they believe in ghosts. Suppose she finds that, among all Americans who are registered to vote, 31.7% are registered Democrats and 27.6% are registered Republicans. Among all registered American voters, the percent of people who are Democrat and who believe in ghosts is 7.0%, the percent of people who are Republicans and who believe in ghosts is 6.1%, and the percent of people who affiliate with other political parties and who believe in ghosts is 9.0%. Label each branch of the tree diagram with the correct probability value. Political party affiliation Believes in ghosts Yes 0.070 Democrat 0.930 No 0.317 Yes 0.061 0.276 Republican 0.939 No 0.407 Yes 0.090 Other 0.910 No Answer Bankarrow_forward
- Two construction companies, Giant and Sky, bid for the right to build in a field. The possible bids are $ 10 Million, $ 20 Million, $ 30 Million, $ 35 Million and $ 40 Million. The winner is the company with the higher bid. The two companies decide that in the case of a tie (equal bids), Giant is the winner and will get the field. Giant has ordered a survey and, based on the report from the survey, concludes that getting the field for more than $ 35 Million is as bad as not getting it (assume loss), except in case of a tie (assume win). Sky is not aware of this survey. (a) State reasons why/how this game can be described as a two-players-zero-sum game (b) Considering all possible combinations of bids, formulate the payoff matrix for the game. (c) Explain what is a saddle point. Verify: does the game have a saddle point? (d) Construct a linear programming model for Company Giant in this game. (e) Produce an appropriate code to solve the linear programming model in part (d). (f)…arrow_forwardA father and his three children decide to hold a vote to select an after dinner activity. They will either see a play or a movie. If the majority of the family agrees on a preferred activity, then they will do that activity. If two family members vote to see a play and the other two family members vote to watch a movie, then (since the father will pay for the activity), the father's vote will be used to break the tie. (a) How many winning coalitions are there in this situation? (b) Find one of the children's Banzhaf power index.arrow_forwardYour class gets to elect a representative for the school council. The two choices are Lizzy and Michael. Polling of the class shows that Polly is preferred by 53% to 47% over Michael. However, before the vote is held, a new choice for representative is put forth by a student: Rodney. Many of the students that prefer Polly, would rather have Rodney. The results of the vote are below. Michael 45% Polly Rodney 35% 17% What statement below is correct about adding a third choice to the plurality vote? Rodney did not win the vote, but it had no effect on drawing enough support away from Polly to make Michael the winner, even though a majority of students preferred Polly over Michael when there were two choices. Rodney did not win the vote, but it draws enough support away from Polly to make Michael the winner, even though a majority of students preferred Polly over Michael when there were two choices. Rodney did not win the vote, so because of this Polly should win the vote over Michael. a…arrow_forward
- Question. The number of first-year students who were admitted and accepted for the 2022 fall semester at Pitt was 4927. Of those: 3431 were admitted to the Dietrich School of Arts and Sciences, 661 were admitted to the School of Engineering, 402 were admitted to the College of Business Administration, 253 were admitted to the School of Computing and Information, 180 were admitted to the School of Nursing. Part a ) Given the size of the group of first-year students (here, we can call this the population), can we assume independence if we choose a sample of two students? Possible answer choices: No because N < 10n Yes because N > 10n Part b) If you were to choose two students at random and assume that the sampling is approximately independent, what is the probability that both students are in the College of Business Administration? (report to 3 decimal places as a proportion.)arrow_forwardA course is taught by three different instructors: Professor A, Professor B, and Professor C. All students in the course must take a comprehensive final exam. Students of Professor A pass the final 85 % of the time. Students of Professor B pass the final 60 % of the time. Students of Professor C pass the final 20 % of the time. Further, 50 % of the students in this course are students of Professor A, 30 % are students of Professor B, and the remaining 20 % are students of Professor C. Given that a randomly selected student passed the final exam, find the probability that he or she was a student of Professor C. Give the probability as a decimal, and if rounding give to 4 decimal places. The probability isarrow_forwardIn a certain year, the U.S. Senate was made up of 53 Democrats, 45 Republicans, and 2 Independents who caucus with the Democrats. In a survey of the U.S. Senate conducted at that time, every senator was asked whether he or she owned at least one gun. Of the Democrats, 18 declared themselves gun owners; of the Republicans, 27 of them declared themselves gun owners; none of the Independents owned guns. If a senator participating in that survey was picked at random and turned out to be a gun owner, what was the probability that he or she was a Democrat? (Round your answer to four decimal places.)arrow_forward
- Suppose that after the 2020 presidential election there are three races that are too close to call: Wisconsin,Michigan, and Pennsylvania. In order to become president, a candidate must receive 270 electoral votes ormore. Wisconsin has 10 electoral votes, Michigan has 16, and Pennsylvania has 20. Suppose that in theother decided races, Democrats have 259 electoral votes and Republicans have 233. The Democrat has an80% chance of winning Wisconsin, a 50% chance of winning Michigan, and a 10% chance of winningPennsylvania. A statistician defines a random variableXto be +1 if the Democrat wins,−1 if theRepublican wins, and 0 if neither candidate reaches 270 electoral votes. Find the probability densityfunction ofX. (Hint: Make this easier by figuring out the scenario in which the Republican wins or there isa tie!)arrow_forwardA housing development offers homes with four different options. The homes were built with one choice from each of the options below. Number of Bedrooms: Two Bedrooms, Three Bedrooms, or Four Bedrooms Number of Bathrooms: One Bathroom, Two Bathrooms, or Three Bathrooms Number of Floors: One Floor or Two Floors Type of Yard: Grass or Desert Landscaping There are an equal number of houses with each combination of options.You would like to buy a house with three bedrooms or four bedrooms, three bathrooms, one floor, and grass or desert landscaping. If there is only one house left to buy, what is the probability that it has what you are looking for?arrow_forwardOne game at a carnival is called “Duck Pond.” This game consists of a large number of ducks that arefloating through an oval-shaped trough. A sign claims that 20% of the ducks have a blue dot on thebottom of them, 20% have a red dot, 20% have a green dot, 20% have a yellow dot, and 20% have anorange dot. Players pay to select one duck, show the color to the game attendant, replace the duck, spinaround once, and then select a second duck. If the dot on the bottom of the second duck matches the dotthat was on the bottom of the first duck, the player wins. Otherwise, the player loses. a) Are the events “color of the first duck” and “color of the second duck” independent? Explain. b) You want to perform a simulation to estimate the probability of winning this game, assuming theduck colors are distributed as claimed. Describe how you could use a table of random digits tocarry out this simulation without needing to skip any digits. c) Perform 10 trials of the simulation described in part (b)…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
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