Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
3rd Edition
ISBN: 9780134689555
Author: Edgar Goodaire, Michael Parmenter
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 7.4, Problem 2E
If the die in Exercise 1 is tossed twice, find the probability that
[BB] the sum of the numbers appearing is 8;
the sum of the numbers appearing is at least 11;
the sum of the numbers appearing is even;
[BB] the numbers that appear differ by 4;
the numbers that appear differ by at least 4.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Answer number one
answer number 4
3. Bayesian Inference – Updating Beliefs
A medical test for a rare disease has the following characteristics:
Sensitivity (true positive rate): 99%
Specificity (true negative rate): 98%
The disease occurs in 0.5% of the population.
A patient receives a positive test result.
Questions:
a) Define the relevant events and use Bayes’ Theorem to compute the probability that the patient actually has the disease.b) Explain why the result might seem counterintuitive, despite the high sensitivity and specificity.c) Discuss how prior probabilities influence posterior beliefs in Bayesian inference.d) Suppose a second, independent test with the same accuracy is conducted and is also positive. Update the probability that the patient has the disease.
Chapter 7 Solutions
Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
Ch. 7.1 - True/False Questions 5!=120Ch. 7.1 - Prob. 2TFQCh. 7.1 - Prob. 3TFQCh. 7.1 - Prob. 4TFQCh. 7.1 - Prob. 5TFQCh. 7.1 - Prob. 6TFQCh. 7.1 - True/False Questions
7. An r-permutation of n...Ch. 7.1 - Prob. 8TFQCh. 7.1 - Prob. 9TFQCh. 7.1 - True/False Questions There are 4!=24 ways in which...
Ch. 7.1 - The answers to exercises marked [BB] can be found...Ch. 7.1 - The answers to exercises marked [BB] can be found...Ch. 7.1 - The answers to exercises marked [BB] can be found...Ch. 7.1 - The answers to exercises marked [BB] can be found...Ch. 7.1 - The answers to exercises marked [BB] can be found...Ch. 7.1 - The answers to exercises marked [BB] can be found...Ch. 7.1 - In how many ways can ten boys and four girls sit...Ch. 7.1 - Prob. 8ECh. 7.1 - Prob. 9ECh. 7.1 - Prob. 10ECh. 7.1 - The answers to exercises marked [BB] can be found...Ch. 7.1 - [BB] In how many ways can two couples, the...Ch. 7.1 - Repeat Exercise 12, assuming, in each part, that a...Ch. 7.1 - Prob. 14ECh. 7.1 - Prob. 15ECh. 7.1 - Prob. 16ECh. 7.1 - 17. (a) In how many numbers with seven distinct...Ch. 7.1 - Prob. 18ECh. 7.2 - True/False Questions
Ch. 7.2 - Prob. 2TFQCh. 7.2 - Prob. 3TFQCh. 7.2 - Prob. 4TFQCh. 7.2 - Prob. 5TFQCh. 7.2 - Prob. 6TFQCh. 7.2 - Prob. 7TFQCh. 7.2 - Prob. 8TFQCh. 7.2 - Prob. 9TFQCh. 7.2 - Prob. 1ECh. 7.2 - The answers to exercises marked [BB] can be found...Ch. 7.2 - Prob. 3ECh. 7.2 - The answers to exercises marked [BB] can be found...Ch. 7.2 - [BB] In how many ways can Tom, Billie, and Peter...Ch. 7.2 - The answers to exercises marked [BB] can be found...Ch. 7.2 - 7. In a popular lottery known as Lotto 6/49, a...Ch. 7.2 - Prob. 8ECh. 7.2 - The answers to exercises marked [BB] can be found...Ch. 7.2 - The answers to exercises marked [BB] can be found...Ch. 7.2 - Prob. 11ECh. 7.2 - Prob. 12ECh. 7.2 - Prob. 13ECh. 7.2 - Prob. 14ECh. 7.2 - The answers to exercises marked [BB] can be found...Ch. 7.2 - 16. The head of the Department of Mathematical...Ch. 7.2 - The answers to exercises marked [BB] can be found...Ch. 7.2 - Prob. 18ECh. 7.2 - Prob. 19ECh. 7.2 - Prob. 20ECh. 7.2 - Prob. 21ECh. 7.2 - The answers to exercises marked [BB] can be found...Ch. 7.2 - Prob. 23ECh. 7.2 - Prob. 24ECh. 7.2 - Prob. 25ECh. 7.2 - Prob. 26ECh. 7.3 - Prob. 1TFQCh. 7.3 - Prob. 2TFQCh. 7.3 - Prob. 3TFQCh. 7.3 - Prob. 4TFQCh. 7.3 - Prob. 5TFQCh. 7.3 - Prob. 6TFQCh. 7.3 - Prob. 7TFQCh. 7.3 - Prob. 8TFQCh. 7.3 - Prob. 9TFQCh. 7.3 - Prob. 10TFQCh. 7.3 - Prob. 1ECh. 7.3 - Prob. 2ECh. 7.3 - Prob. 3ECh. 7.3 - Prob. 4ECh. 7.3 - [BB] A fair coin is tossed six times. Find the...Ch. 7.3 - Prob. 6ECh. 7.3 - The next two exercises refer to Lotto 6/49, a...Ch. 7.3 - 8. In Lotto 6/49, find the probability of...Ch. 7.3 - 9. [BB] A basket contains five red balls, four...Ch. 7.3 - Prob. 10ECh. 7.3 - [BB] Repeat Exercise 9 assuming the first ball...Ch. 7.3 - 12. Repeat Exercise 10 assuming the two balls are...Ch. 7.3 - Prob. 13ECh. 7.3 - Prob. 14ECh. 7.3 - Prob. 15ECh. 7.3 - Prob. 16ECh. 7.3 - Find the probability that an integer selected at...Ch. 7.3 - Prob. 18ECh. 7.3 - Prob. 19ECh. 7.3 - Prob. 20ECh. 7.3 - Prob. 21ECh. 7.3 - Prob. 22ECh. 7.3 - Prob. 23ECh. 7.3 - Prob. 24ECh. 7.3 - (See Exercise 11 of Section 7.1), find the...Ch. 7.3 - Prob. 26ECh. 7.3 - Prob. 27ECh. 7.3 - Prob. 28ECh. 7.3 - Prob. 29ECh. 7.3 - Prob. 30ECh. 7.3 - Prob. 31ECh. 7.3 - Prob. 32ECh. 7.4 - Prob. 1TFQCh. 7.4 - Prob. 2TFQCh. 7.4 - Prob. 3TFQCh. 7.4 - Prob. 4TFQCh. 7.4 - Prob. 5TFQCh. 7.4 - Prob. 6TFQCh. 7.4 - Prob. 7TFQCh. 7.4 - Prob. 8TFQCh. 7.4 - Prob. 9TFQCh. 7.4 - Prob. 10TFQCh. 7.4 - Prob. 1ECh. 7.4 - 2. If the die in Exercise 1 is tossed twice, find...Ch. 7.4 - Prob. 3ECh. 7.4 - Prob. 4ECh. 7.4 - Prob. 5ECh. 7.4 - Prob. 6ECh. 7.4 - [BB] A coin has P(H)=14. If it is tossed six times...Ch. 7.4 - The answers to exercises marked [BB] can be found...Ch. 7.4 - Prob. 9ECh. 7.4 - Prob. 10ECh. 7.4 - Prob. 11ECh. 7.4 - Prob. 12ECh. 7.4 - Prob. 13ECh. 7.4 - Prob. 14ECh. 7.4 - 15. A fair coin is tossed n times. Let A be the...Ch. 7.4 - Prob. 16ECh. 7.4 - Prob. 17ECh. 7.4 - Prob. 18ECh. 7.4 - Prob. 19ECh. 7.4 - Prob. 20ECh. 7.4 - Prob. 21ECh. 7.4 - 22. (a) Find the probability that everyone in a...Ch. 7.4 - Prob. 23ECh. 7.4 - Prob. 24ECh. 7.4 - [BB] Given 70P20=.3,40P50=.5, and 10P40=.9, find...Ch. 7.4 - [BB] The probability that two persons aged 20 and...Ch. 7.4 - Prob. 27ECh. 7.4 - Prob. 28ECh. 7.4 - 29. [BB] Consumers in the town of Trout River have...Ch. 7.4 - Prob. 30ECh. 7.4 - 31. A new three- screen cinema has just opened in...Ch. 7.5 - Prob. 1TFQCh. 7.5 - (Answers can be found in the back of the book.)
2....Ch. 7.5 - (Answers can be found in the back of the book.)...Ch. 7.5 - Prob. 4TFQCh. 7.5 - Prob. 5TFQCh. 7.5 - Prob. 6TFQCh. 7.5 - Prob. 7TFQCh. 7.5 - Prob. 8TFQCh. 7.5 - Prob. 9TFQCh. 7.5 - Prob. 10TFQCh. 7.5 - The answers to exercises marked [BB] can be found...Ch. 7.5 - Prob. 2ECh. 7.5 - Prob. 3ECh. 7.5 - Prob. 4ECh. 7.5 - Prob. 5ECh. 7.5 - 6. Twenty varieties of chocolates are available...Ch. 7.5 - Prob. 7ECh. 7.5 - The answers to exercises marked [BB] can be found...Ch. 7.5 - The answers to exercises marked [BB] can be found...Ch. 7.5 - Prob. 10ECh. 7.5 - 11. (a) [BB] In how many ways can ten red balls,...Ch. 7.5 - The answers to exercises marked [BB] can be found...Ch. 7.5 - Prob. 13ECh. 7.5 - Find the number of arrangements of the letters of...Ch. 7.5 - Prob. 15ECh. 7.5 - Prob. 16ECh. 7.5 - Show that there is a one-to-one correspondence...Ch. 7.5 - The answers to exercises marked [BB] can be found...Ch. 7.5 - Prob. 19ECh. 7.6 - (Answers can be found in the back of the book.)
1....Ch. 7.6 - Prob. 2TFQCh. 7.6 - Prob. 3TFQCh. 7.6 - Prob. 4TFQCh. 7.6 - Prob. 5TFQCh. 7.6 - Prob. 6TFQCh. 7.6 - (Answers can be found in the back of the book.)
7....Ch. 7.6 - Prob. 8TFQCh. 7.6 - Prob. 9TFQCh. 7.6 - Prob. 10TFQCh. 7.6 - Prob. 1ECh. 7.6 - Prob. 2ECh. 7.6 - Prob. 3ECh. 7.6 - Prob. 4ECh. 7.6 - Prob. 5ECh. 7.6 - Prob. 6ECh. 7.6 - [BB] In how many ways can the integers 1 through 9...Ch. 7.6 - Without any calculation, prove that...Ch. 7.6 - Prob. 9ECh. 7.6 - Prob. 10ECh. 7.6 - Prob. 11ECh. 7.6 - Prob. 12ECh. 7.7 - (Answers can be found in the back of the book.)
1....Ch. 7.7 - Prob. 2TFQCh. 7.7 - Prob. 3TFQCh. 7.7 - Prob. 4TFQCh. 7.7 - Prob. 5TFQCh. 7.7 - Prob. 6TFQCh. 7.7 - Prob. 7TFQCh. 7.7 - Prob. 8TFQCh. 7.7 - Prob. 9TFQCh. 7.7 - Prob. 10TFQCh. 7.7 - Prob. 1ECh. 7.7 - The answers to exercises marked [BB] can be found...Ch. 7.7 - Prob. 3ECh. 7.7 - Prob. 4ECh. 7.7 - Prob. 5ECh. 7.7 - Prob. 6ECh. 7.7 - Prob. 7ECh. 7.7 - Prob. 8ECh. 7.7 - Prob. 9ECh. 7.7 - Prob. 10ECh. 7.7 - Prob. 11ECh. 7.7 - Prob. 12ECh. 7.7 - Prob. 13ECh. 7.7 - Sequences of integers, {xn},{yn},n0, are defined...Ch. 7.7 - Prob. 15ECh. 7.7 - The answers to exercises marked [BB] can be found...Ch. 7.7 - Prob. 17ECh. 7.7 - 18. Prove the Binominal Theorem by mathematical...Ch. 7.7 - Prob. 19ECh. 7.7 - Prob. 20ECh. 7.7 - Prob. 21ECh. 7.7 - Prob. 22ECh. 7.7 - Prob. 23ECh. 7.7 - 24. There are n books in a line on a shelf and...Ch. 7.7 - Prob. 25ECh. 7 - Prove that 2nP(2n,n) for all integers n1.Ch. 7 - In how many ways can seven boys and six girls...Ch. 7 - Do Exercise 2 again with circle instead of row.Ch. 7 - How many permutations of the letters a, b, c, d,...Ch. 7 - 5. (a) In how many permutations of the 26...Ch. 7 - 6. Find an expression for the number of five-card...Ch. 7 - A committee of seven is to be chosen from eight...Ch. 7 - In how many ways can 12 people from four groups of...Ch. 7 - A car manufacturer is forced to admit that the...Ch. 7 - 10. Ten students find themselves in an...Ch. 7 - 11. For Christmas, Gail wants to buy each of her...Ch. 7 - 12. A Middle East peace conference will be...Ch. 7 - Prob. 13RECh. 7 - Frank wants to buy 12 muffins and finds seven...Ch. 7 - Twelve ships enter the St. Johns harbor one after...Ch. 7 - 16. A candy merchant carries bubble gum balls in...Ch. 7 - 17. In how many ways can the letters of the word...Ch. 7 - 18. In how many ways can five rings be put onto...Ch. 7 - Find the coefficient of x6 in (16x212x)12....Ch. 7 - Find the coefficient of x6 in (16x212x)12....Ch. 7 - 21. Prove that for any .
Ch. 7 - Give a verbal argument for the truth of the...Ch. 7 - 23. Find a simple expression for .
Ch. 7 - Show that (2nn) is even for all n1.Ch. 7 - On the day before midterm break, 20 of the 32...Ch. 7 - 26. A fair coin is tossed n times. Prove that...
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
- answer number 6arrow_forwardanswer number 2arrow_forward4. Linear Regression - Model Assumptions and Interpretation A real estate analyst is studying how house prices (Y) are related to house size in square feet (X). A simple linear regression model is proposed: The analyst fits the model and obtains: • Ŷ50,000+150X YBoB₁X + € • R² = 0.76 • Residuals show a fan-shaped pattern when plotted against fitted values. Questions: a) Interpret the slope coefficient in context. b) Explain what the R² value tells us about the model's performance. c) Based on the residual pattern, what regression assumption is likely violated? What might be the consequence? d) Suggest at least two remedies to improve the model, based on the residual analysis.arrow_forward
- 5. Probability Distributions – Continuous Random Variables A factory machine produces metal rods whose lengths (in cm) follow a continuous uniform distribution on the interval [98, 102]. Questions: a) Define the probability density function (PDF) of the rod length.b) Calculate the probability that a randomly selected rod is shorter than 99 cm.c) Determine the expected value and variance of rod lengths.d) If a sample of 25 rods is selected, what is the probability that their average length is between 99.5 cm and 100.5 cm? Justify your answer using the appropriate distribution.arrow_forward2. Hypothesis Testing - Two Sample Means A nutritionist is investigating the effect of two different diet programs, A and B, on weight loss. Two independent samples of adults were randomly assigned to each diet for 12 weeks. The weight losses (in kg) are normally distributed. Sample A: n = 35, 4.8, s = 1.2 Sample B: n=40, 4.3, 8 = 1.0 Questions: a) State the null and alternative hypotheses to test whether there is a significant difference in mean weight loss between the two diet programs. b) Perform a hypothesis test at the 5% significance level and interpret the result. c) Compute a 95% confidence interval for the difference in means and interpret it. d) Discuss assumptions of this test and explain how violations of these assumptions could impact the results.arrow_forward1. Sampling Distribution and the Central Limit Theorem A company produces batteries with a mean lifetime of 300 hours and a standard deviation of 50 hours. The lifetimes are not normally distributed—they are right-skewed due to some batteries lasting unusually long. Suppose a quality control analyst selects a random sample of 64 batteries from a large production batch. Questions: a) Explain whether the distribution of sample means will be approximately normal. Justify your answer using the Central Limit Theorem. b) Compute the mean and standard deviation of the sampling distribution of the sample mean. c) What is the probability that the sample mean lifetime of the 64 batteries exceeds 310 hours? d) Discuss how the sample size affects the shape and variability of the sampling distribution.arrow_forward
- An airplane flies due west at an airspeed of 428 mph. The wind blows in the direction of 41° south of west at 50 mph. What is the ground speed of the airplane? What is the bearing of the airplane? 428 mph 41° 50 mph a. The ground speed of the airplane is b. The bearing of the airplane is mph. south of west.arrow_forwardRylee's car is stuck in the mud. Roman and Shanice come along in a truck to help pull her out. They attach one end of a tow strap to the front of the car and the other end to the truck's trailer hitch, and the truck starts to pull. Meanwhile, Roman and Shanice get behind the car and push. The truck generates a horizontal force of 377 lb on the car. Roman and Shanice are pushing at a slight upward angle and generate a force of 119 lb on the car. These forces can be represented by vectors, as shown in the figure below. The angle between these vectors is 20.2°. Find the resultant force (the vector sum), then give its magnitude and its direction angle from the positive x-axis. 119 lb 20.2° 377 lb a. The resultant force is (Tip: omit degree notations from your answers; e.g. enter cos(45) instead of cos(45°)) b. It's magnitude is lb. c. It's angle from the positive x-axis isarrow_forwardComplete the table below. For solutions, round to the nearest whole number.arrow_forward
- A biologist is investigating the effect of potential plant hormones by treating 20 stem segments. At the end of the observation period he computes the following length averages: Compound X = 1.18 Compound Y = 1.17 Based on these mean values he concludes that there are no treatment differences. 1) Are you satisfied with his conclusion? Why or why not? 2) If he asked you for help in analyzing these data, what statistical method would you suggest that he use to come to a meaningful conclusion about his data and why? 3) Are there any other questions you would ask him regarding his experiment, data collection, and analysis methods?arrow_forwardBusinessarrow_forwardAnswer first questionarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Probability & Statistics (28 of 62) Basic Definitions and Symbols Summarized; Author: Michel van Biezen;https://www.youtube.com/watch?v=21V9WBJLAL8;License: Standard YouTube License, CC-BY
Introduction to Probability, Basic Overview - Sample Space, & Tree Diagrams; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=SkidyDQuupA;License: Standard YouTube License, CC-BY