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, Problem 23SE
posethatAandBareeventswthprobabilitiesp(A) = 3/4andp(B) = 1/3.
- What is the largest p(A fl B) can be? What is the smallest it can be? Give examples to show that both extremes for p(A"B)are possible.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
One estimate of the proportion of children with autism in the United States is 1 in 100 (Source: http://www.cbsnews.com/stories/2009/10/05/health/main5363192.shtml). Suppose you are interested in the rate of autism among current school-aged children in Utah. You collect a sample of 400 children between the ages of 5 and 18 and find that three have had a previous diagnosis of an autism disorder. You plan to calculate a 95% confidence interval estimator of the proportion of school-aged children in Utah who have ever had a diagnosis of an autism disorder.
Which of the following is the most likely reason you would use a Wilson estimator to calculate the confidence interval estimator?
It is uncomfortable to define having been diagnosed with autism as a success.
It is possible that if even the actual proportion in Utah is 1%, your sample may only have very few children who have had a previous diagnosis of an autism disorder.
It is an easier way to calculate the confidence…
In an experiment to compare the tensile strengths of I = 6 different types of copper wire, J = 5 samples of each type were used. The between-samples and within-samples estimates of σ² were computed as MSTr = 2623.3
and MSE = 1193.2, respectively. Use the F test at level 0.05 to test Ho: μ₁ = M2 μ6 versus Ha: at least two μ's are unequal.
=
...=
You can use the Distribution Calculators page in SALT to find critical values and/or p-values to answer parts of this question.
Calculate the test statistic. (Round your answer to two decimal places.)
f =
What can be said about the P-value for the test?
P-value>0.100
0.050 P-value < 0.100
0.010 P-value < 0.050
0.001 P-value < 0.010
P-value <0.001
State the conclusion in the problem context.
Reject Ho. The data indicates there is not a difference in the mean tensile strengths.
Fail to reject Ho. The data indicates a difference in the mean tensile strengths.
Reject Ho. The data indicates a difference in the mean tensile strengths.
Fail to reject…
show step by step answer
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
- Write the given third order linear equation as an equivalent system of first order equations with initial values. Use Y1 = Y, Y2 = y', and y3 = y". - - √ (3t¹ + 3 − t³)y" — y" + (3t² + 3)y' + (3t — 3t¹) y = 1 − 3t² \y(3) = 1, y′(3) = −2, y″(3) = −3 (8) - (888) - with initial values Y = If you don't get this in 3 tries, you can get a hint.arrow_forwardThe system of first order differential equations y₁ = -4y1 - 1y2 y2 = 1y1 - 2y2 where y1(0) = −8, y2(0) = 6 has solution yı(t) = Y2(t) =arrow_forwardQuestion 2 1 pts Let A be the value of the triple integral SSS. (x³ y² z) dV where D is the region D bounded by the planes 3z + 5y = 15, 4z — 5y = 20, x = 0, x = 1, and z = 0. Then the value of sin(3A) is -0.003 0.496 -0.408 -0.420 0.384 -0.162 0.367 0.364arrow_forward
- Question 1 Let A be the value of the triple integral SSS₂ (x + 22) = 1 pts dV where D is the region in 0, y = 2, y = 2x, z = 0, and the first octant bounded by the planes x z = 1 + 2x + y. Then the value of cos(A/4) is -0.411 0.709 0.067 -0.841 0.578 -0.913 -0.908 -0.120arrow_forwardProblem 2-6. Need help on why its 1.22arrow_forwardScenario: As a data analyst for a retail company, you are tasked with examining the relationship between televisions screen size, and prices. Your analysis will involve both correlation and regression methods to quantify and interpret this relationship Make a Scatterplot of screen size vs. price. Explain in one sentence, does there appear to be a positive or a negative correlation between price and screen size? Paste a snapshot of the plot here. Please do not copy paste. Question 1: What is the value of correlation coefficient between screen size and price? Discuss the direction of the relationship (positive, negative, or zero relationship). Also discuss the strength of the relationship Estimate the relationship between screen size and price using a simple linear regression model and interpret the estimated coefficients. In your interpretation, tell the dollar amount by which price will change for each unit of increase in screen size. (The answer for the second part of this…arrow_forward
- In the xy-plane, the graphs of the linear function and the exponential function E both pass through the points (0,2) and (1,6) The function f is given by f(x) = L(x) - E(x). What is the maximum value of f? A 0.007 B 0.172 C 0.540 D 1.002arrow_forwardTasks: A company manufactures two electronic products: Chipsets and LCD. Each product contributes differently to the profit. The production process is subject to constraints related to labour, manufacturing space, raw materials, and production time. You are required to determine the optimal production quantities for each product to maximize profit: • Develop and formulate a Linear programming model for the variables and constraints from the above context as given in Table 1 & 2. Assume Right-Hand Side (R.H.S) values for all elements and find the maximum profit and optimal variable values using graphical method (40%). Table I Variables Chipsets Profit Per Unit Assume as per convenience and Model Fit Assume as per convenience and Model Fit dictions: On LCD Table II Constraints Labour Manufacturing Space Raw Materials Production Time Units No of Labors Square Meters Kilograms Minutes Identify the feasible region and construct the graph using the graphical method. Evaluate, present. Find…arrow_forwardvery time you conduct a hypothesis test, there are four possible outcomes of your decision to reject or not reject the null hypothesis: (1) You don’t reject the null hypothesis when it is true, (2) you reject the null hypothesis when it is true, (3) you don’t reject the null hypothesis when it is false, and (4) you reject the null hypothesis when it is false. Consider the following analogy: You are an airport security screener. For every passenger who passes through your security checkpoint, you must decide whether to select the passenger for further screening based on your assessment of whether he or she is carrying a weapon. Suppose your null hypothesis is that the passenger has a weapon. As in hypothesis testing, there are four possible outcomes of your decision: (1) You select the passenger for further inspection when the passenger has a weapon, (2) you allow the passenger to board her flight when the passenger has a weapon, (3) you select the passenger for further inspection when…arrow_forward
- EKS C ALEKS - Kim Johnson - Ch 6S × 4 www-awy.aleks.com alekscgi/x/sl.exe/16_u-lgNs/kr7j8FB)--BjuvZG weRMign 4tCy83MpSgONH0-ovaPm-Zym e Chrome isn't your default browser Set as default Ch 6 Sec 4 Homework Question 4 of 4 (1 point) | Question Attempt: 2 of Unlimited ✓ 2 ✓ 3 = 4 Stress at work: In a poll conducted by the General Social Survey, 81% of respondents said that their jobs were sometimes or always stressful. Two hundred workers are chosen at random. Use the TI-84 Plus calculator as needed. Round your answer to at least four decimal places. (a) Approximate the probability that 155 or fewer workers find their jobs stressful. (b) Approximate the probability that more than 145 workers find their jobs stressful. (c) Approximate the probability that the number of workers who find their jobs stressful is between 154 and 172 inclusive. Part 1 of 3 The probability that 155 or fewer workers find their jobs stressful is 0.1207 Part 2 of 3 bility that more than 145 workers find their jobs…arrow_forwardA case-control (or retrospective) study was conducted to investigate a relationship between the colors of helmets worn by motorcycle drivers and whether they are injured or killed in a crash. Results are given in the accompanying table. Using a 0.01 significance level, test the claim that injuries are independent of helmet color. Color of Helmet Black White Yellow Red Blue Controls (not injured) 499 373 32 159 79 Cases (injured 221 108 8 66 38 or killed) Click here to view the chi-square distribution table. Chi-square distribution table Area to the Right of the Critical Value Degrees of Freedom 0.995 0.99 0.975 0.95 0.90 0.10 0.05 0.025 0.01 0.005 C. Ho: Injuries and neimet color are dependent H₁: Injuries and helmet color are independent D. Ho: Whether a crash occurs and helmet color are dependent 1 0.001 0.004 0.016 2.706 3.841 5.024 6.635 7.879 2 0.010 0.020 0.051 0.103 0.211 4.605 5.991 7.378 9.210 10.597 3 0.072 0.115 0.216 0.352 0.584 6.251 7.815 9.348 11.345 12.838 4 0.207 0.297…arrow_forwardConduct the hypothesis test and provide the test statistic and the critical value, and state the conclusion. A person drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 200 times. Here are the observed frequencies for the outcomes of 1, 2, 3, 4, 5, and 6, respectively: 28, 32, 46, 39, 29, 26. Use a 0.025 significance level to test the claim that the outcomes are not equally likely. Does it appear that the loaded die behaves differently than a fair die? Click here to view the chi-square distribution table. The test statistic is (Round to three decimal places as needed.) Chi-square distribution table Area to the Right of the Critical Value Degrees of Freedom 0.995 0.99 0.975 0.95 0.90 0.10 0.05 0.025 0.01 0.005 1 0.001 0.004 0.016 2.706 3.841 5.024 6.635 2 0.010 0.020 0.051 0.103 0.211 4.605 5.991 7.378 9.210 7.879 10.597 3 0.072 0.115 0.216 0.352 0.584 6.251 7.815 9.348 11.345 12.838 4 0.207 0.297 0.484 0.711 1.064 7.779 9.488 11.143 13.277 14.860 5…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
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
Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
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
Elements Of Modern Algebra
Algebra
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Cengage Learning,
Statistics 4.1 Point Estimators; Author: Dr. Jack L. Jackson II;https://www.youtube.com/watch?v=2MrI0J8XCEE;License: Standard YouTube License, CC-BY
Statistics 101: Point Estimators; Author: Brandon Foltz;https://www.youtube.com/watch?v=4v41z3HwLaM;License: Standard YouTube License, CC-BY
Central limit theorem; Author: 365 Data Science;https://www.youtube.com/watch?v=b5xQmk9veZ4;License: Standard YouTube License, CC-BY
Point Estimate Definition & Example; Author: Prof. Essa;https://www.youtube.com/watch?v=OTVwtvQmSn0;License: Standard Youtube License
Point Estimation; Author: Vamsidhar Ambatipudi;https://www.youtube.com/watch?v=flqhlM2bZWc;License: Standard Youtube License