DISCRETE MATHEMATICS+ITS APPL. (LL)-W/A
8th Edition
ISBN: 9781260521337
Author: ROSEN
Publisher: MCG
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 7.2, Problem 38E
38.A pair of dice is rolled in a remote location and when you ask an honest observer whether at least one die came up six, this honest observer answers in the affirmative.
- What is the probability that the sum of the numbers that came up on the two dice is seven, given the information provided by the honest observer?
- Suppose that the honest observer tells us that at least one die came up five. What is the probability the sum of the numbers that came up on the dice is seven, given this information?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Chatgpt means downvote
Because Chatgpt gives wrong answer
One bulb manufacturer claims an average bulb life of 1,600 hours. It is suspected that the actual average is significantly lower. To verify this, a sample of 49 bulbs is selected and the life of each bulb is measured. A sample mean of 1,500 hours and a standard deviation of 120 hours were obtained from them.
Can you be sure, at 5% significance, that the mean life is less than what the manufacturer claims?
The specification calls for the dimension of a certain mechanical part to be 0.55 inches. A random sample of 35 parts taken from a large batch showed a mean 0.54 in. with a deviation of 0.05 in.
Can it be concluded, at 1% significance, that the batch of parts meets the required specification?
Chapter 7 Solutions
DISCRETE MATHEMATICS+ITS APPL. (LL)-W/A
Ch. 7.1 - i. What is the probability that a card selected at...Ch. 7.1 - t istheprobability that a fair die comes up six...Ch. 7.1 - t is the probability that a randomly selected...Ch. 7.1 - What is the probability7that a randomly selected...Ch. 7.1 - t is the probability that the sum of the numbers...Ch. 7.1 - t is the probability that a card selected at...Ch. 7.1 - t is the probability that when a coin is flipped...Ch. 7.1 - t is the probability that a five-card poker hand...Ch. 7.1 - t is the probability that a five-card poker hand...Ch. 7.1 - t is the probability that a five-card poker hand...
Ch. 7.1 - Prob. 11ECh. 7.1 - t is the probability that afive-card poker hand...Ch. 7.1 - t is the probability tliat afive-card poker hand...Ch. 7.1 - t istheprobability that a five-card poker hand...Ch. 7.1 - t is theprobabilifrthatafive-cardpoker hand...Ch. 7.1 - t is the probability7that a five-card poker hand...Ch. 7.1 - Prob. 17ECh. 7.1 - Mat is the probability' that a five-card poker...Ch. 7.1 - Prob. 19ECh. 7.1 - probabihh’thatafiM^Ch. 7.1 - Prob. 21ECh. 7.1 - t is the probability that a positive integer not...Ch. 7.1 - t is the probability that a positive integer not...Ch. 7.1 - Prob. 24ECh. 7.1 - - Find the probability of winning a lottery by...Ch. 7.1 - 26.Find the pr obabilitj- of selecting none of the...Ch. 7.1 - Prob. 27ECh. 7.1 - Prob. 28ECh. 7.1 - Prob. 29ECh. 7.1 - Prob. 30ECh. 7.1 - Prob. 31ECh. 7.1 - Prob. 32ECh. 7.1 - i$theprobabilitytiiatAbby,Barry,andSy^...Ch. 7.1 - 34.Mat is the probability' that Bo, Colleen, Jeff,...Ch. 7.1 - roulette, a wheel with 38 numbers is spun. Of...Ch. 7.1 - ch is more likely: rolling a total of 8 when two...Ch. 7.1 - ch is more likely: rolling a total of 9 when hvo...Ch. 7.1 - A player in the Mega Millions lottery picks five...Ch. 7.1 - a player buys a Mega Millions ticket in many...Ch. 7.1 - A player in the Powerball lottery picks five...Ch. 7.1 - Aplayer in the Powerball lottery (see Exercise 40)...Ch. 7.1 - Two events E i and E2are calledindependentifp(Etfl...Ch. 7.1 - Prob. 43ECh. 7.1 - Suppose that instead of three doors, there are...Ch. 7.1 - s problem was posed by the Chevalier de Mere and...Ch. 7.2 - Prob. 1ECh. 7.2 - Prob. 2ECh. 7.2 - Prob. 3ECh. 7.2 - w that conditions (2) and (22) are met under...Ch. 7.2 - A pair of dice is loaded. The probability that a 4...Ch. 7.2 - t is the probability of these events when we...Ch. 7.2 - t is the probability of these events when we...Ch. 7.2 - 8.What is the probability of these events when we...Ch. 7.2 - t is the probability of these events when we...Ch. 7.2 - What is the probability of these events when we...Ch. 7.2 - pose, that £ and F are. events such that d(£)=0.7...Ch. 7.2 - pose that £ and Fare events such thatp(£) = 0.8...Ch. 7.2 - w that if £ and F are events, thenpfEn F) >p(E) +...Ch. 7.2 - Use mathematical induction to prove the following...Ch. 7.2 - w that if £x, £2,Enare events from afinite sample...Ch. 7.2 - Show that iff and f are independent events,...Ch. 7.2 - 17,It £ and F are independent events, prove or...Ch. 7.2 - What is the probability that hvo people chosen at...Ch. 7.2 - Mat is the probability that two people chosen at...Ch. 7.2 - Prob. 20ECh. 7.2 - Prob. 21ECh. 7.2 - February 29 occurs only inleap years, Years...Ch. 7.2 - ^Tiat is the conditional probabilitv that exactly...Ch. 7.2 - What is the. conditional probabilih' that exactly...Ch. 7.2 - Prob. 25ECh. 7.2 - Let Ebe the event that aranmly generated bit...Ch. 7.2 - Prob. 27ECh. 7.2 - a8. Assume that the probability a child is a boy...Ch. 7.2 - A group of six people play the game of “ odd...Ch. 7.2 - Find the probability that a randomly generated bit...Ch. 7.2 - Find the probability that a family with five...Ch. 7.2 - Prob. 32ECh. 7.2 - Prob. 33ECh. 7.2 - Find each of the following probabilities...Ch. 7.2 - d each of the following probabilities...Ch. 7.2 - Prob. 36ECh. 7.2 - Prob. 37ECh. 7.2 - 38.A pair of dice is rolled in a remote location...Ch. 7.2 - This exercise employs the probabilistic method to...Ch. 7.2 - Dense a Monte Carlo algorithm that determines...Ch. 7.2 - pseudocode to write out the probabilistic...Ch. 7.3 - i.Suppose that £ andFare events in a sample space...Ch. 7.3 - Suppose that Land Fare events in a sample space...Ch. 7.3 - 3.Suppose that Frida selects a ball by first...Ch. 7.3 - 4.Suppo s e that Ann selects a ball by first...Ch. 7.3 - Prob. 5ECh. 7.3 - Prob. 6ECh. 7.3 - Prob. 7ECh. 7.3 - 8,Suppose that one person in 10,000 people has a...Ch. 7.3 - Suppose that 8% of the patients tested in a clinic...Ch. 7.3 - io,Suppose that 4% of the patients tested in a...Ch. 7.3 - ...Ch. 7.3 - ...Ch. 7.3 - Prob. 13ECh. 7.3 - Prob. 14ECh. 7.3 - In this exercise we will use Bayes' theorem to...Ch. 7.3 - Prob. 16ECh. 7.3 - Prob. 17ECh. 7.3 - 18.Suppose that a Bayesian spam filter is trained...Ch. 7.3 - 19,Suppose that a Bayesian spam filter is trained...Ch. 7.3 - Prob. 20ECh. 7.3 - ,Suppose that a Bayesian spam filter is trained on...Ch. 7.3 - Suppose that we have prior information concerning...Ch. 7.3 - Prob. 23ECh. 7.4 - t is the expected number of heads that come up...Ch. 7.4 - t is the expected number of heads that come up...Ch. 7.4 - t is the expected number of times a 6 appears when...Ch. 7.4 - A coin is biased so that the probability a head...Ch. 7.4 - ^Tiat is the expected sum of the numbers that...Ch. 7.4 - Prob. 6ECh. 7.4 - final exam of a discrete mathematics course...Ch. 7.4 - t is the expected sum of the numbers that appear...Ch. 7.4 - Prob. 9ECh. 7.4 - Suppose that we flip a fair coin until either it...Ch. 7.4 - Suppose that we roll a fair die until a 6 conies...Ch. 7.4 - pose that we roll a fair die until a 6 comes up....Ch. 7.4 - pose thatwerollapairoffair dice...Ch. 7.4 - Show that the sum of the probabilities of a random...Ch. 7.4 - Show that if the random variable A'has the...Ch. 7.4 - Prob. 16ECh. 7.4 - Prob. 17ECh. 7.4 - Prob. 18ECh. 7.4 - Prob. 19ECh. 7.4 - Show that if J2,...,Xnare mutually independent...Ch. 7.4 - What is the expected value of the sum of the...Ch. 7.4 - as.Provethelaw of total expectations.Ch. 7.4 - Prob. 23ECh. 7.4 - Prob. 24ECh. 7.4 - A run is a maximal sequence of successes in a...Ch. 7.4 - a6.Let J(s) be a random variable, where I(s) is a...Ch. 7.4 - What is the variance of the number of heads that...Ch. 7.4 - t is the variance ot the number of times a 6...Ch. 7.4 - LetXnbe the random variable that equals the number...Ch. 7.4 - w that ifXand Fare independent random variables,...Ch. 7.4 - Prob. 31ECh. 7.4 - Pronde an example that shows that the variance of...Ch. 7.4 - pose that A\ andX2are independent Bernoulli trials...Ch. 7.4 - Prove the general caseofTheoremy. That is, show...Ch. 7.4 - Prob. 35ECh. 7.4 - Prob. 36ECh. 7.4 - Prob. 37ECh. 7.4 - pose that the number of cans of soda pop filled in...Ch. 7.4 - 39.Suppose that the number of aluminum cans...Ch. 7.4 - pose the probabilitvthatxis the...Ch. 7.4 - In this exercise we derive an estimate of the...Ch. 7.4 - Prob. 42ECh. 7.4 - to is the variance of the number of fixed...Ch. 7.4 - Prob. 44ECh. 7.4 - Prob. 45ECh. 7.4 - Prob. 46ECh. 7.4 - Prob. 47ECh. 7.4 - Prob. 48ECh. 7.4 - Prob. 49ECh. 7 - Define the probability of an event when all...Ch. 7 - WTiat conditions should be met by the...Ch. 7 - Define, the conditional probability’ of an event £...Ch. 7 - Prob. 4RQCh. 7 - tois a random variable? toare the possible values...Ch. 7 - Prob. 6RQCh. 7 - Explain how the average-case computational...Ch. 7 - Prob. 8RQCh. 7 - What does the linearity of expectations of random...Ch. 7 - Prob. 10RQCh. 7 - Prob. 11RQCh. 7 - Prob. 12RQCh. 7 - Prob. 13RQCh. 7 - What is the variance of the sum of n independent...Ch. 7 - Prob. 15RQCh. 7 - Prob. 1SECh. 7 - 2012, a player in the Mega Millions lottery picks...Ch. 7 - 2012, a player in the Powerball lottery picks five...Ch. 7 - t is the probability that a hand of 13 cards...Ch. 7 - t is the probability that a 13-card bridge hand...Ch. 7 - t is the probability that a seven-card poker hand...Ch. 7 - What is the expected value of the number that...Ch. 7 - What is the expected value of the number that...Ch. 7 - Suppose that a pair of fair octahedral dice is...Ch. 7 - io.Suppose that a pair offaiir dodecahedral diceis...Ch. 7 - ii.Supp o s e that a fair standard (cubic) die and...Ch. 7 - Prob. 12SECh. 7 - (mpeople!n>3!play“oddp™ut’todeadeMo^...Ch. 7 - Prob. 14SECh. 7 - posethatmandnarepositiYeintegers.Bat is...Ch. 7 - pose thatEt, E2,Enarenevents with p(£j) >o fori...Ch. 7 - Prob. 17SECh. 7 - t is the probability that when a fair coin is...Ch. 7 - t is the probability that a randomly selected bit...Ch. 7 - t is the probability that a randomly selected bit...Ch. 7 - sider the following game. A per son flips a coin...Ch. 7 - pose that n halls are tossed intobbins so that...Ch. 7 - posethatAandBareeventswthprobabilitiesp(A) =...Ch. 7 - posethat/l andB are events...Ch. 7 - all fromDefinition jinSection 7,2that the events...Ch. 7 - ...Ch. 7 - Prob. 27SECh. 7 - Prob. 28SECh. 7 - Prob. 29SECh. 7 - Prob. 30SECh. 7 - Prob. 31SECh. 7 - Prob. 32SECh. 7 - Prob. 33SECh. 7 - maximum satisfiability problemasks for an...Ch. 7 - Prob. 35SECh. 7 - The following method can be used to generate a...Ch. 7 - Prob. 1CPCh. 7 - Prob. 2CPCh. 7 - Prob. 3CPCh. 7 - Prob. 4CPCh. 7 - Prob. 5CPCh. 7 - ...Ch. 7 - Prob. 7CPCh. 7 - Prob. 8CPCh. 7 - Prob. 9CPCh. 7 - ulaterepeated trials oftheMoufr Hall Three-Door...Ch. 7 - Prob. 11CPCh. 7 - Prob. 1CAECh. 7 - Prob. 2CAECh. 7 - Prob. 3CAECh. 7 - Prob. 4CAECh. 7 - Prob. 5CAECh. 7 - Prob. 6CAECh. 7 - Prob. 7CAECh. 7 - Prob. 8CAECh. 7 - cribe the origins of probability theory and the...Ch. 7 - Prob. 2WPCh. 7 - 3.Discuss the probability' of winning when you...Ch. 7 - estigate the game of craps and discuss the...Ch. 7 - Prob. 5WPCh. 7 - Prob. 6WPCh. 7 - lain how Erdos and Renvi first used the...Ch. 7 - cuss the different types of probabilistic...
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
- Let = , -2 X(t) = [ 6° 2t e -3e -2t X(t)= 2e-2t -6e- -2t 9]. Verify that the matrix ✗(t) is a fundamental matrix of the given linear system. Determine a constant matrix C such that the given matrix Ŷ (t) can be represented as Ŷ(t) = X(t)C. C = help (matrices) The determinant of the matrix C is help (numbers) which is Choose . Therefore, the matrix ✗(t) is Choose Book: Section 3.3 of Notes on Diffy Qsarrow_forwardA manufacturer produces a wire rope of a certain type, which has a breaking strength of not more than 300 kg. A new and cheaper process is discovered which is desired to be employed, provided that the wire rope thus produced has an average breaking strength greater than 300 kg. If a random sample of 26 wires produced with the new process has given a mean of 304.5 kg and a standard deviation of 15 kg, should the manufacturer adopt the new process?arrow_forward5. mit answer urces Use Simpson's Rule and all the data in the following table to estimate the value of the 31 integral f(x) dx. 25 25 26 27 28 29 30 31 f(x) 4 44 4 -9 -2 9 2 5 (Round your answer to within two decimal places if necessary, but do not round until your final computation.) Simpson's Rule Approximation: PROGRES Score Completi 30 i Submit answer T The Weather Channel UP DELL FB F4 F5 F9 9. F10arrow_forward
- Find the most general real-valued solution to the linear system of differential equations + C2 7-430 help (formulas) help (matrices) [*] »B] [8]: In the phase plane, this system is best described as a source/unstable node O sink / stable node saddle center point / ellipses spiral source spiral sink none of these Book: Section 3.5 of Notes on Diffy Qsarrow_forwardFind the most general real-valued solution to the linear system of differential equations x x(t) y(t) = +C2 [*] [] [B] In the phase plane, this system is best described as a source/unstable node sink/stable node saddle center point / ellipses spiral source spiral sink none of these Book: Section 3.5 of Notes on Diffy Qs help (formulas) help (matrices)arrow_forwardFind the most general real-valued solution to the linear system of differential equations x(t) -9 8' [J - j (-8-8 y(t) In the phase plane, this system is best described as a source/unstable node sink/stable node saddle center point / ellipses spiral source spiral sink none of these Book: Section 3.5 of Notes on Diffy Qs -12 11 help (formulas) help (matrices)arrow_forward
- Find the most general real-valued solution to the linear system of differential equations x(t) -2 7-730 --8-8 y(t) = In the phase plane, this system is best described as a source/unstable node sink / stable node saddle center point / ellipses spiral source spiral sink ☐ none of these Book: Section 3.5 of Notes on Diffy Qs 1 help (formulas) help (matrices)arrow_forwardConsider the system of differential equations dx 8 3 x Y dt 4 -- (0) + (1) (음)- (0) dy 18 y. dt For this system, the eigenvalues are help (numbers) Enter as a comma separated list. How do the solution curves of the system above behave? All of the solutions curves would converge towards 0 (sink/stable node). All of the solution curves would run away from 0 (source/unstable node). The solution curves would race towards zero and then veer away towards infinity (saddle point). The solution curves converge to different points. The solution to the above differential equation with initial values x(0) = 5, y(0) = 3 is x(t) = help (formulas) y(t) = help (formulas) Book: Section 3.5 of Notes on Diffy Qsarrow_forwardConsider the system of differential equations Verify that x' x, x(0) = x(t) = c1e5t H + Cze³t [] is a solution to the system of differential equations for any choice of the constants C1 and C2. Find values of C1 and C2 that solve the given initial value problem. (According to the uniqueness theorem, you have found the unique solution of ' = Px, x(0) = 0). H e³t (t) = ( \ ) · e³ {}] + () ·³ [1] Book: Section 3.3 of Notes on Diffy Qs help (numbers)arrow_forward
- Find the most general real-valued solution to the linear system of differential equations [5 -6 x = -10|| x(t) [*] [B] • [8] = C1 y(t) In the phase plane, this system is best described as a source/unstable node O sink / stable node saddle center point / ellipses spiral source spiral sink none of these Book: Section 3.5 of Notes on Diffy Qs help (formulas) help (matrices)arrow_forwardConsider the system of higher order differential equations y″ = t¯¹y' + 7y – tz + (sint)z' + e5t, z" = y — 3z'. Rewrite the given system of two second order differential equations as a system of four first order linear differential equations of the form ÿ' = P(t)ÿ+ g(t). Use the following change of variables y' [Y] Y1 Y2 Y3 LY4_ help (formulas) help (matrices) Book: Section 3.3 of Notes on Diffy Qs [y1(t)] [ y(t)] Y2(t) y' (t) ÿ(t) = = Y3(t) z(t) Y₁(t)] [z'(t)]arrow_forwardCalculate the eigenvalues of this matrix: [21 12 A 24 -21 You'll probably want to use a calculator or computer to estimate the roots of the polynomial that defines the eigenvalues. The system has two real eigenvalues 1 and 2 where \1<\2 smaller eigenvalue \1 = help (numbers) associated eigenvector v1 larger eigenvalue 2 = = help (matrices) help (numbers) associated eigenvector v2 If x' = = B help (matrices) A is a differential equation, how do the solution curves behave? A. The solution curves diverge from different points on parallel paths. B. The solution curves would race towards zero and then veer away towards infinity. (saddle point) C. The solution curves converge to different points on parallel paths. D. All of the solution curves would run away from 0. (source / unstable node) E. All of the solutions curves would converge towards 0. (sink / stable node) Book: Section 3.5 of Notes on Diffy Qsarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
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