Math

StatisticsProbability and Statistics for Engineering and the SciencesA system consists of two identical pumps, #1 and #2. If one pump fails, the system will still operate. However, because of the added strain, the remaining pump is now more likely to fail than was originally the case. That is, r 5 P (#2 fails | #1 fails). P (#2 fails) = q. If at least one pump fails by the end of the pump design life in 7% of all systems and both pumps fail during that period in only 1%, what is the probability that pump #1 will fail during the pump design life?BuyFind*arrow_forward*

9th Edition

Jay L. Devore

Publisher: Cengage Learning

ISBN: 9781305251809

Chapter 2.4, Problem 52E

Textbook Problem

A system consists of two identical pumps, #1 and #2. If one pump fails, the system will still operate. However, because of the added strain, the remaining pump is now more likely to fail than was originally the case. That is, *r* 5 *P*(#2 fails | #1 fails). *P*(#2 fails) = *q.* If at least one pump fails by the end of the pump design life in 7% of all systems and both pumps fail during that period in only 1%, what is the probability that pump #1 will fail during the pump design life?

Expert Solution

To determine

Find the probability that the pump #1 fails during pump design life.

**Given info:**

The system has two identical pumps #1 and #2. The system will operate even if one pump fails. The pumps fail due to the strain that is,

**Calculation:**

Here *A*_{1} denotes the event that pump #1 fails, *A*_{2} denotes the event that pump #2 fails,

Since the two pumps were identical, so

*Addition rule:*

For any two events *A* and *B,*

Probability and Statistics for Engineering and the Sciences

Show all chapter solutions

Ch. 2.1 - Four universities1, 2, 3, and 4are participating...Ch. 2.1 - Suppose that vehicles taking a particular freeway...Ch. 2.1 - Three components are connected to form a system as...Ch. 2.1 - Each of a sample of four home mortgages is...Ch. 2.1 - A family consisting of three personsA, B, and...Ch. 2.1 - A college library has five copies of a certain...Ch. 2.1 - An academic department has just completed voting...Ch. 2.1 - An engineering construction firm is currently...Ch. 2.1 - Use Venn diagrams to verify the following two...Ch. 2.1 - a. In Example 2.10, identify three events that are...

Ch. 2.2 - A mutual fund company offers its customers a...Ch. 2.2 - Consider randomly selecting a student at a large...Ch. 2.2 - A computer consulting firm presently has bids out...Ch. 2.2 - Suppose that 55% of all adults regularly consume...Ch. 2.2 - Consider the type of clothes dryer (gas or...Ch. 2.2 - An individual is presented with three different...Ch. 2.2 - Let A denote the event that the next request for...Ch. 2.2 - A wallet contains five 10 bills, four 5 bills, and...Ch. 2.2 - Human visual inspection of solder joints on...Ch. 2.2 - A certain factory operates three different shifts....Ch. 2.2 - An insurance company offers four different...Ch. 2.2 - The route used by a certain motorist in commuting...Ch. 2.2 - The computers of six faculty members in a certain...Ch. 2.2 - Show that if one event A is contained in another...Ch. 2.2 - The three most popular options on a certain type...Ch. 2.2 - A certain system can experience three different...Ch. 2.2 - An academic department with five faculty members...Ch. 2.2 - In Exercise 5, suppose that any incoming...Ch. 2.3 - As of April 2006, roughly 50 million .com web...Ch. 2.3 - A friend of mine is giving a dinner party. His...Ch. 2.3 - The composer Beethoven wrote 9 symphonies, 5 piano...Ch. 2.3 - An electronics store is offering a special price...Ch. 2.3 - Again consider a Little League team that has 15...Ch. 2.3 - Computer keyboard failures can be attributed to...Ch. 2.3 - A production facility employs 10 workers on the...Ch. 2.3 - An academic department with five faculty members...Ch. 2.3 - An experimenter is studying the effects of...Ch. 2.3 - A sonnet is a 14-line poem in which certain...Ch. 2.3 - A box in a supply room contains 15 compact...Ch. 2.3 - Three molecules of type A, three of type B, three...Ch. 2.3 - An ATM personal identification number (PIN)...Ch. 2.3 - A starting lineup in basketball consists of two...Ch. 2.3 - In five-card poker, a straight consists of five...Ch. 2.3 - Show that (nk)=(nnk). Give an interpretation...Ch. 2.4 - The population of a particular country consists of...Ch. 2.4 - Suppose an individual is randomly selected from...Ch. 2.4 - Return to the credit card scenario of Exercise 12...Ch. 2.4 - Reconsider the system defect situation described...Ch. 2.4 - The accompanying table gives information on the...Ch. 2.4 - A department store sells sport shirts in three...Ch. 2.4 - According to a July 31, 2013, posting on cnn.com...Ch. 2.4 - A system consists of two identical pumps, #1 and...Ch. 2.4 - A certain shop repairs both audio and video...Ch. 2.4 - In Exercise 13, Ai = {awarded project i}, for i =...Ch. 2.4 - Deer ticks can be carriers of either Lyme disease...Ch. 2.4 - For any events A and B with P(B) 0, show that...Ch. 2.4 - If P(B|A) P(B), show that P(B|A) P(B). [Hint:...Ch. 2.4 - Show that for any three events A, B, and C with...Ch. 2.4 - At a certain gas station, 40% of the customers use...Ch. 2.4 - Seventy percent of the light aircraft that...Ch. 2.4 - Components of a certain type are shipped to a...Ch. 2.4 - Blue Cab operates 15% of the taxis in a certain...Ch. 2.4 - For customers purchasing a refrigerator at a...Ch. 2.4 - The Reviews editor for a certain scientific...Ch. 2.4 - A large operator of timeshare complexes requires...Ch. 2.4 - Consider the following information about travelers...Ch. 2.4 - There has been a great deal of controversy over...Ch. 2.4 - A friend who lives in Los Angeles makes frequent...Ch. 2.4 - In Exercise 59, consider the following additional...Ch. 2.5 - Reconsider the credit card scenario of Exercise 47...Ch. 2.5 - An oil exploration company currently has two...Ch. 2.5 - In Exercise 13, is any Ai independent of any other...Ch. 2.5 - If A and B are independent events, show that A and...Ch. 2.5 - The proportions of blood phenotypes in the U.S....Ch. 2.5 - One of the assumptions underlying the theory of...Ch. 2.5 - In October, 1994, a flaw in a certain Pentium chip...Ch. 2.5 - An aircraft seam requires 25 rivets. The seam will...Ch. 2.5 - A boiler has five identical relief valves. The...Ch. 2.5 - Two pumps connected in parallel fail independently...Ch. 2.5 - Consider the system of components connected as in...Ch. 2.5 - Refer back to the series-parallel system...Ch. 2.5 - Consider independently rolling two fair dice, one...Ch. 2.5 - Components arriving at a distributor are checked...Ch. 2.5 - Consider purchasing a system of audio components...Ch. 2.5 - A quality control inspector is examining newly...Ch. 2.5 - a. A lumber company has just taken delivery on a...Ch. 2.5 - Consider randomly selecting a single individual...Ch. 2.5 - The probability that an individual randomly...Ch. 2.5 - Suppose identical tags are placed on both the left...Ch. 2 - A certain legislative committee consists of 10...Ch. 2 - A factory uses three production lines to...Ch. 2 - An employee of the records office at a certain...Ch. 2 - One satellite is scheduled to be launched from...Ch. 2 - A transmitter is sending a message by using a...Ch. 2 - Individual A has a circle of five close friends...Ch. 2 - According to the article Optimization of...Ch. 2 - A chemical engineer is interested in determining...Ch. 2 - Five friendsAllison, Beth, Carol, Diane, and...Ch. 2 - Fasteners used in aircraft manufacturing are...Ch. 2 - Jay and Maurice are playing a tennis match. In one...Ch. 2 - A system consists of two components. The...Ch. 2 - The accompanying table categorizing each student...Ch. 2 - a. A certain company sends 40% of its overnight...Ch. 2 - A company uses three different assembly linesA1,...Ch. 2 - Disregarding the possibility of a February 29...Ch. 2 - One method used to distinguish between granitic...Ch. 2 - A subject is allowed a sequence of glimpses to...Ch. 2 - In a Little League baseball game, team As pitcher...Ch. 2 - Four engineers, A, B, C, and D, have been...Ch. 2 - A particular airline has 10 a.m. flights from...Ch. 2 - Consider four independent events A1, A2, A3, and...Ch. 2 - A box contains the following four slips of paper,...Ch. 2 - Show that if A1, A2, and A3 are independent...

Find more solutions based on key concepts

Show solutions Draw an example of a production possibilities frontier for Robinson Crusoe, a shipwrecked sailor who spends his...

Principles of Economics (MindTap Course List)

(The Long-Run Industry Supply Curve) A normal good is being produced in a constant-cost, perfectly competitive ...

ECON: MICRO4 (New, Engaging Titles from 4LTR Press)

The Kroger Company is one of the largest grocery retailers in the United States, with over 2000 grocery stores ...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

If more Americans adopted a live for today approach to life, how would this affect saving, investment, and the ...

Principles of Macroeconomics (MindTap Course List)

Three students have each saved 1,000. Each has an investment opportunity in which he or she can invest up to 2,...

Brief Principles of Macroeconomics (MindTap Course List)

Why should policymakers think about incentives?

Principles of Microeconomics (MindTap Course List)

Financial statements and closing entries The Gorman Group is a financial planning services firm owned and opera...

Financial & Managerial Accounting

Describe the similarities and differences between limit checks and reasonable checks. Give examples where each ...

Accounting Information Systems

Appendix 2 Cost of goods sold Identify the errors in the: following schedule of the cost of goods sold for the ...

Corporate Financial Accounting

CAPITAL BUDGETING CRITERIA: ETHICAL CONSIDERATIONS A mining company is considering a new project. Because the m...

Fundamentals of Financial Management (MindTap Course List)

REALIZED RATES OF RETURN Stocks A and 13 have the following historical returns: Year Slock As Returns, rA Stock...

Fundamentals of Financial Management, Concise Edition (MindTap Course List)

How is the production of services similar to the production of manufactured goods?

Foundations of Business (MindTap Course List)

Where are the jobs? Even though you may not be in the market at the moment, become familiar with the kinds of a...

Essentials of Business Communication (MindTap Course List)

If a companys board of directors wants management to maximize shareholder wealth, should the CEOs compensation ...

Fundamentals Of Financial Management, Concise Edition (mindtap Course List)

( Appendix 6B) Inventory Costing Methods: Periodic Inventory System The inventory accounting records for Lee En...

Cornerstones of Financial Accounting

SOC A researcher is studying changes in the student body at her university and has selected a random sample of ...

Essentials Of Statistics

The following scores are the ages for a random sample of n = 32 drivers who were issued parking tickets in Chic...

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Critical Thinking Suppose two events A and B are independent, with P(A)0andP(B)0. By working through the follow...

Understanding Basic Statistics

In a study examining the effect of alcohol on reaction time, Liguori and Robinson (2001) found that even modera...

Statistics for The Behavioral Sciences (MindTap Course List)

Finding pH The hydrogen ion concentrations in cheeses range from 4.0 107 M to 1.6 105 M. Find the correspondi...

Precalculus: Mathematics for Calculus (Standalone Book)

Think About It In Exercises 79-82, L' Hospitals Rule is used incorrectly. Describe the error. limx23x2+4x+1x2x2...

Calculus: Early Transcendental Functions

Evaluate the integral. 11.0122x2+3x+1dx

Calculus: Early Transcendentals

Use the guidelines of this section to sketch the curve. y=sinx2+cosx

Single Variable Calculus: Early Transcendentals, Volume I

In Exercises 1316, find the distance between the given pairs of points. (a,a)and(b,b)

Finite Mathematics and Applied Calculus (MindTap Course List)

Use a table of values to estimate the value of the limit. If you have a graphing device, use it to confirm your...

Single Variable Calculus

Discuss the continuity of f(x)={ x+21x314x2,3x5.

Calculus: An Applied Approach (MindTap Course List)

Find an equation of the sphere that passes through the point (4, 3, 1) and has center (3, 8, 1).

Multivariable Calculus

Rewrite each expression in Exercises 116 as a single rational expression, simplified as much as possible. xx313...

Finite Mathematics

For Problems 64-78, translate each English phrase into an algebraic expression and use n to represent the unkno...

Intermediate Algebra

Lobbyists Spending Lobbyists try to persuade legislators to propose, pass, or defeat legislation or to change e...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

4547 Find the point at which the line intersects the given plane. 5x=y/2=z+2; 10x7y+3z+24=0

Calculus (MindTap Course List)

Calculate the missing income statement items for Exercise 3, Target, and Exercise 4, Advance Auto Parts. Comple...

Contemporary Mathematics for Business & Consumers

One of the zeros is given for each of the following polynomial. Find the other zeros in the field of complex nu...

Elements Of Modern Algebra

Find the three cube roots for each of the following complex numbers. Leave your answers in trigonometric form. ...

Trigonometry (MindTap Course List)

7. Find the maximum value of the function subject to the condition .

Mathematical Applications for the Management, Life, and Social Sciences

The recommended safety angle of a ladder against a building is 78. A 10 -m ladder will be used. How high up on ...

Elementary Technical Mathematics

In Exercises 55 and 56, use the inclusion-exclusion formula to answer each application. 56. A college finds tha...

Mathematical Excursions (MindTap Course List)

Review Exercises Given: FABHCD EADGCB Prove: ABCD is a

Elementary Geometry For College Students, 7e

Finding Volume Using a Change of Variables In Exercises 23-30, use a change of variables to find the volume of ...

Calculus: Early Transcendental Functions (MindTap Course List)

Constant Force In Exercises 5-8, determine the work done by the constant force. The locomotive of a freight tra...

Calculus of a Single Variable

For the limit limx2(x33x+4)=6 illustrate Definition 2 by finding values of that correspond =0.2 and 0.1. Def...

Single Variable Calculus: Early Transcendentals

LICENSE PLATE NUMBERS Over the years, the state of California has used different combinations of letters of the...

Finite Mathematics for the Managerial, Life, and Social Sciences

The authors of the paper Mean Platelet Volume Could Be Possible Biomarker in Early Diagnosis and Monitoring of ...

Introduction To Statistics And Data Analysis

A cross-country runner jogs at a rate of 15 feet per second. If she runs 300 feet from A to B, 450 feet from B ...

Elementary Geometry for College Students

True or False:
is a convergent series.

Study Guide for Stewart's Multivariable Calculus, 8th

True or False:
The graph at the right is the graph of a function.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

The website for the Bed and Breakfast Inns of North America gets approximately sevenvisitors per minute (Time, ...

Statistics for Business & Economics, Revised (MindTap Course List)

Can a research study be an experiment without a control group? Can a study be an experiment without controlling...

Research Methods for the Behavioral Sciences (MindTap Course List)

Describe how participant reactivity can be a threat to external validity; that is, how can participant reactivi...

Research Methods for the Behavioral Sciences (MindTap Course List)

Solve for the unknown value in each of the following proportions. Check each answer. Round the answers to 3 dec...

Mathematics For Machine Technology

Self Check Find a fourth-degree polynomial function with real coefficients and i as a zero of multiplicity 2.

College Algebra (MindTap Course List)

Integration by Parts State whether you would use integration by parts to find each integral. If so, identify wh...

Calculus (MindTap Course List)

Verifying Stokess Theorem In Exercises 3-6, verify Stokess Theorem by evaluating CFdr as a line integral and as...

Multivariable Calculus

Online Education. One of the biggest changes in higher education in recent years has been the growth of online ...

Essentials Of Statistics For Business & Economics

In exercise 1, the following estimated regression equation based on 10 observations was presented.
Here SST = ...

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)

Spring/Mass Systems: Free Undamped Motion A mass weighing 20 pounds stretches a spring 6 inches. The mass is in...

A First Course in Differential Equations with Modeling Applications (MindTap Course List)

Prove that each of the properties in 21-29 is an invariant for graph isomorphism. Assume that n, m, and k are a...

Discrete Mathematics With Applications

Frequency of Musical Notes Counting sharps and flats, there are 12 notes in an octave on a standard piano. If o...

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

Explain the difference between simple interest and compound interest.

Mathematics: A Practical Odyssey

Use the following information to answer the next three exercises The average lifetime of a certain new cell pho...

Introductory Statistics

For the following exercises, use the graph of f(x)=x2 to graph each transformed function g. 88. g(x)=x21

Calculus Volume 1