Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Finite Mathematics and Applied Calculus (MindTap Course List)
Electric Car Sales In 2014 the probability that a randomly chosen electric car sold in the United States was manufactured by Tesla was .30, while the probability that it was manufactured by Nissan was .35.42 What is the probability that a randomly chosen electric car was manufactured by neither company?Hybrid Auto Sales In 2010 the probability that a randomly chosen hybrid vehicle sold in the United States was manufactured by Ford was .12, while the probability that it was manufactured by Nissan was .02.43 What is the probability that a randomly chosen hybrid vehicle was manufactured by neither company?Student Admissions Exercises 6984 are based on the following table, which shows the profile, by the math section of the SAT Reasoning Test, of admitted students at UCLA for the Fall 2014 semester:44 SAT Reasoning TestMath Section 700800 600699 500599 400499 200399 Total Admitted 8,398 3,517 1,410 358 9 13,692 Not Admitted 16,599 18,363 13,119 6,714 1,652 56,447 Total Applicants 24,997 21,880 14,529 7,072 1,661 70,139 Determine the probabilities of the following events. (Round your answers to the nearest .01.) [HinT: Example 6.] An applicant was admitted.Student Admissions Exercises 6984 are based on the following table, which shows the profile, by the math section of the SAT Reasoning Test, of admitted students at UCLA for the Fall 2014 semester:44 SAT Reasoning TestMath Section 700800 600699 500599 400499 200399 Total Admitted 8,398 3,517 1,410 358 9 13,692 Not Admitted 16,599 18,363 13,119 6,714 1,652 56,447 Total Applicants 24,997 21,880 14,529 7,072 1,661 70,139 Determine the probabilities of the following events. (Round your answers to the nearest .01.) [HinT: Example 6.] An applicant had a Math SAT below 400.71E72E73E74EStudent Admissions Exercises 6984 are based on the following table, which shows the profile, by the math section of the SAT Reasoning Test, of admitted students at UCLA for the Fall 2014 semester:44 SAT Reasoning TestMath Section 700800 600699 500599 400499 200399 Total Admitted 8,398 3,517 1,410 358 9 13,692 Not Admitted 16,599 18,363 13,119 6,714 1,652 56,447 Total Applicants 24,997 21,880 14,529 7,072 1,661 70,139 Determine the probabilities of the following events. (Round your answers to the nearest .01.) [HinT: Example 6.] An applicant had a Math SAT in the range 500599 or was admitted.76E77EStudent Admissions Exercises 6984 are based on the following table, which shows the profile, by the math section of the SAT Reasoning Test, of admitted students at UCLA for the Fall 2014 semester:44 SAT Reasoning TestMath Section 700800 600699 500599 400499 200399 Total Admitted 8,398 3,517 1,410 358 9 13,692 Not Admitted 16,599 18,363 13,119 6,714 1,652 56,447 Total Applicants 24,997 21,880 14,529 7,072 1,661 70,139 Determine the probabilities of the following events. (Round your answers to the nearest .01.) [HinT: Example 6.] An applicant neither had a Math SAT of 700 or above nor was admitted.79EStudent Admissions Exercises 6984 are based on the following table, which shows the profile, by the math section of the SAT Reasoning Test, of admitted students at UCLA for the Fall 2014 semester:44 SAT Reasoning TestMath Section 700800 600699 500599 400499 200399 Total Admitted 8,398 3,517 1,410 358 9 13,692 Not Admitted 16,599 18,363 13,119 6,714 1,652 56,447 Total Applicants 24,997 21,880 14,529 7,072 1,661 70,139 Determine the probabilities of the following events. (Round your answers to the nearest .01.) [HinT: Example 6.] An applicant who had a Math SAT of 700 or above was admitted.81E82E83E84E85E86E87ESwords and Sorcery Lance the Wizard has been informed that tomorrow there will be a 50% chance of encountering the evil Myrmidons and a 20% chance of meeting up with the dreadful Balrog. Moreover, Hugo the Elf has predicted that there is a 10% chance of encountering both tomorrow. What is the probability that Lance will be lucky tomorrow and encounter neither the Myrmidons nor the Balrog?Public Health A study shows that 80% of the population was vaccinated against the Venusian flu but 2% of the vaccinated population got the flu anyway. If 10% of the total population got this flu, what percent of the population either got the vaccine or got the disease?90E91E92E93E94E95E96E97E98E99E100E101E102E103E104ERecall from Example 1 that whenever Suzan sees a bag of marbles, she grabs a handful at random. In Exercises 110, she has seen a bag containing four red marbles, three green ones, two white ones, and one purple one. She grabs five of them. Find the probabilities of the following events, expressing each as a fraction in lowest terms. [HinT: See Example 1.] She has all the red ones.Recall from Example 1 that whenever Suzan sees a bag of marbles, she grabs a handful at random. In Exercises 110, she has seen a bag containing four red marbles, three green ones, two white ones, and one purple one. She grabs five of them. Find the probabilities of the following events, expressing each as a fraction in lowest terms. [HinT: See Example 1.] She has none of the red ones.Recall from Example 1 that whenever Suzan sees a bag of marbles, she grabs a handful at random. In Exercises 110, she has seen a bag containing four red marbles, three green ones, two white ones, and one purple one. She grabs five of them. Find the probabilities of the following events, expressing each as a fraction in lowest terms. [HinT: See Example 1.] She has at least one white one.Recall from Example 1 that whenever Suzan sees a bag of marbles, she grabs a handful at random. In Exercises 110, she has seen a bag containing four red marbles, three green ones, two white ones, and one purple one. She grabs five of them. Find the probabilities of the following events, expressing each as a fraction in lowest terms. [HinT: See Example 1.] She has at least one green one.Recall from Example 1 that whenever Suzan sees a bag of marbles, she grabs a handful at random. In Exercises 110, she has seen a bag containing four red marbles, three green ones, two white ones, and one purple one. She grabs five of them. Find the probabilities of the following events, expressing each as a fraction in lowest terms. [HinT: See Example 1.] She has two red ones and one of each of the other colors.Recall from Example 1 that whenever Suzan sees a bag of marbles, she grabs a handful at random. In Exercises 110, she has seen a bag containing four red marbles, three green ones, two white ones, and one purple one. She grabs five of them. Find the probabilities of the following events, expressing each as a fraction in lowest terms. [HinT: See Example 1.] She has two green ones and one of each of the other colors.7E8ERecall from Example 1 that whenever Suzan sees a bag of marbles, she grabs a handful at random. In Exercises 110, she has seen a bag containing four red marbles, three green ones, two white ones, and one purple one. She grabs five of them. Find the probabilities of the following events, expressing each as a fraction in lowest terms. [HinT: See Example 1.] She does not have all the red ones.10EDogs of the Dow The Dogs of the Dow are the stocks listed on the Dow with the highest dividend yield. Exercises 1116 are based on the following table, which shows the top ten stocks of the Dogs of the Dow list for 2015, based on their performance the preceding year.47 [HinT: See Example 2.] Symbol Company Price Yield T aTT 33.59 5.48% VZ Verizon 46.78 4.70% CVX Chevron 112.18 3.82% MCD McDonalds 93.70 3.63% PFE Pfizer 31.15 3.60% GE General Electric 25.27 3.48% MRK Merck 56.79 3.17% CAT Caterpillar 91.53 3.06% XOM ExxonMobil 92.45 2.99% KO Coca-Cola 42.22 2.89% If you selected two of these stocks at random, what is the probability that both the stocks in your selection had yields of 3.75% or more?12E13E14EDogs of the Dow The Dogs of the Dow are the stocks listed on the Dow with the highest dividend yield. Exercises 1116 are based on the following table, which shows the top ten stocks of the Dogs of the Dow list for 2015, based on their performance the preceding year.47 [HinT: See Example 2.] Symbol Company Price Yield T aTT 33.59 5.48% VZ Verizon 46.78 4.70% CVX Chevron 112.18 3.82% MCD McDonalds 93.70 3.63% PFE Pfizer 31.15 3.60% GE General Electric 25.27 3.48% MRK Merck 56.79 3.17% CAT Caterpillar 91.53 3.06% XOM ExxonMobil 92.45 2.99% KO Coca-Cola 42.22 2.89% If your portfolio included 100 shares of PFE and you then purchased 100 shares each of any two companies on the list at random, find the probability that you ended up with a total of 200 shares of PFE.Dogs of the Dow The Dogs of the Dow are the stocks listed on the Dow with the highest dividend yield. Exercises 1116 are based on the following table, which shows the top ten stocks of the Dogs of the Dow list for 2015, based on their performance the preceding year.47 [HinT: See Example 2.] Symbol Company Price Yield T aTT 33.59 5.48% VZ Verizon 46.78 4.70% CVX Chevron 112.18 3.82% MCD McDonalds 93.70 3.63% PFE Pfizer 31.15 3.60% GE General Electric 25.27 3.48% MRK Merck 56.79 3.17% CAT Caterpillar 91.53 3.06% XOM ExxonMobil 92.45 2.99% KO Coca-Cola 42.22 2.89% If your portfolio included 100 shares of PFE and you then purchased 100 shares each of any three companies on the list at random, find the probability that you ended up with a total of 200 shares of PFE.17E18E19EPoker In Exercises 1924 you are asked to calculate the probability of being dealt various poker hands. (Recall that a poker player is dealt 5 cards at random from a standard deck of 52.) Express each of your answers as a decimal rounded to four decimal places unless otherwise stated. [HinT: See Example 3.] Three of a kind: Three cards with the same denomination and two cards with other denominations (different from each other and that of the three). Example: Q, Q, Q, 4, JPoker In Exercises 1924 you are asked to calculate the probability of being dealt various poker hands. (Recall that a poker player is dealt 5 cards at random from a standard deck of 52.) Express each of your answers as a decimal rounded to four decimal places unless otherwise stated. [HinT: See Example 3.] Two pairs: Two cards with one denomination, two with another, and one with a third. Example: 3, 3, Q, Q, 1022E23E24EThe Monkey at the Typewriter Suppose that a monkey is seated at a computer keyboard and randomly strikes the 26 letter keys and the space bar. Find the probability that its first 39 characters (including spaces) will be to be or not to be that is the question. (Leave your answer as a formula.)The Cat on the Piano A standard piano keyboard has 88 different keys. Find the probability that a cat, jumping on 4 keys in sequence and at random (possibly with repetition), will strike the first four notes of Beethovens Fifth Symphony. (Leave your answer as a formula.)27E28ELotteries The Sorry State Lottery requires you to select five different numbers from 0 through 49. (Order is not important.) You are a Big Winner if the five numbers you select agree with those in the drawing, and you are a Small-Fry Winner if four of your five numbers agree with those in the drawing. What is the probability of being a Big Winner? What is the probability of being a Small-Fry Winner? What is the probability that you are either a Big Winner or a Small-Fry winner?Lotteries The Sad State Lottery requires you to select a sequence of three different numbers from 0 through 49. (Order is important.) You are a Winner if your sequence agrees with that in the drawing, and you are a Booby Prize Winner if your selection of numbers is correct but in the wrong order. What is the probability of being a Winner? What is the probability of being a Booby Prize Winner? What is the probability that you are either a Winner or a Booby Prize Winner?Transfers Your company is considering offering 400 employees the opportunity to transfer to its new headquarters in Ottawa, and, as personnel manager, you decide that it would be fairest if the transfer offers are decided by means of a lottery. Assuming that your company currently employs 100 managers, 100 factory workers, and 500 miscellaneous staff, find the following probabilities, leaving the answers as formulas: a. All the managers will be offered the opportunity. b. You will be offered the opportunity.32E33E34E35EElimination Tournaments In a (fictitious) soccer tournament involving the four teams San Diego State, De Paul, Colgate, and Hofstra, find the probability that Hofstra will play Colgate in the finals and win. (Assume that all outcomes are equally likely and that the teams not listed in the first round slots are placed at random.)37E38E39E40E41E42EGraph Searching A graph consists of a collection of nodes (the dots in the figure) connected by edges (line segments from one node to another). A move on a graph is a move from one node to another along a single edge. Find the probability of going from Start to Finish in a sequence of two random moves in the graph shown. (All directions are equally likely.)44E45E46ECommittees An investigatory committee in the Kingdom of Utopia consists of a chief investigator (a Royal Party member), an assistant investigator (a Birthday Party member), two at-large investigators (either party), and five ordinary members (either party). Royal Party member Larry Sifford is hoping to avoid serving on the committee unless he is the Chief Investigator and Otis Taylor, a Birthday Party member, is the Assistant Investigator. The committee is to be selected at random from a pool of 12 candidates (including Larry Sifford and Otis Taylor), half of whom are Royal Party and half of whom are Birthday Party. a. How many different committees are possible? [HinT: See Example 5.] b. How many committees are possible in which Larrys hopes are fulfilled? (This includes the possibility that hes not on the committee at all.) c. What is the probability that hell be happy with a randomly selected committee?Committees A committee is to consist of a chair, three hagglers, and four do-nothings. The committee is formed by choosing randomly from a pool of 10 people and assigning them to the various jobs. a. How many different committees are possible? [HinT: See Example 5.] b. Norman is eager to be the chair of the committee. What is the probability that he will get his wish? c. Normans girlfriend Norma is less ambitious and would be happy to hold any position on the committee provided that Norman is also selected as a committee member. What is the probability that she will get her wish and serve on the committee? d. Norma does not get along with Oona (who is also in the pool of prospective members) and would be most unhappy if Oona were to chair the committee. Find the probability that all Normas wishes will be fulfilled: She and Norman are on the committee, and it is not chaired by Oona.49E50E51E52E53E54EIn Exercises 110, compute the indicated quantity. P(B)=.5,P(AB)=.2 Find P(A|B).2EIn Exercises 110, compute the indicated quantity. P(A|B)=.2,P(B)=.4. Find P(AB).4EIn Exercises 110, compute the indicated quantity. P(A|B)=.4,P(AB)=.3. Find P(B).6EIn Exercises 110, compute the indicated quantity. P(A)=.5,P(B)=.4. A and B are independent. Find P(AB).8EIn Exercises 110, compute the indicated quantity. P(A)=.5,P(B)=.4 A and B are independent. Find P(A|B).10EIn Exercises 1116, fill in the blanks using the named events. [HinT: See Example 2 and the FAQ at the end of the section.] 10% of all Anchovians detest anchovies (D), whereas 30% of all married Anchovians (M) detest them. P()=; P()=12EIn Exercises 1116, fill in the blanks using the named events. [HinT: See Example 2 and the FAQ at the end of the section.] 30% of all lawyers who lost clients (L), were antitrust lawyers (A), whereas 10% of all antitrust lawyers lost clients. P()=; P()=14EIn Exercises 1116, fill in the blanks using the named events. [HinT: See Example 2 and the FAQ at the end of the section.] 55% of those who go out in the midday sun (M) are Englishmen (E), whereas only 5% of those who do not go out in the midday sun are Englishmen. P()=; P()=16E17EIn Exercises 1722, find the conditional probability of the indicated event when two fair dice (one red and one green) are rolled. [HinT: See Example 1.] The sum is 6, given that the green one is either 4 or 3.19E20EIn Exercises 1722, find the conditional probability of the indicated event when two fair dice (one red and one green) are rolled. [HinT: See Example 1.] The sum is 5, given that the dice have opposite parity.In Exercises 1722, find the conditional probability of the indicated event when two fair dice (one red and one green) are rolled. [HinT: See Example 1.] The sum is 6, given that the dice have opposite parity.23E24E25EExercises 2328 require the use of counting techniques from Chapter 7. A bag contains three red marbles, two green ones, one fluorescent pink one, two yellow ones, and two orange ones. Suzan grabs four at random. Find the probability of the indicated event. She gets one of each color other than fluorescent pink, given that she gets the fluorescent pink one.Exercises 2328 require the use of counting techniques from Chapter 7. A bag contains three red marbles, two green ones, one fluorescent pink one, two yellow ones, and two orange ones. Suzan grabs four at random. Find the probability of the indicated event. She gets one of each color other than fluorescent pink, given that she gets at least one red one.Exercises 2328 require the use of counting techniques from Chapter 7. A bag contains three red marbles, two green ones, one fluorescent pink one, two yellow ones, and two orange ones. Suzan grabs four at random. Find the probability of the indicated event. She gets at least two red ones, given that she gets at least one green one.In Exercises 2932, supply the missing quantities. [HinT: See Example 3 and the discussion preceding it.]30EIn Exercises 2932, supply the missing quantities. [HinT: See Example 3 and the discussion preceding it.]In Exercises 2932, supply the missing quantities. [HinT: See Example 3 and the discussion preceding it.]In Exercises 3336, say whether the given pair of events are independent, mutually exclusive, or neither. A: Your new skateboard design is a success. B: Your new skateboard design is a failure.34EIn Exercises 3336, say whether the given pair of events are independent, mutually exclusive, or neither. A: Your new skateboard design is a success. B: Your competitors new skateboard design is a failure.In Exercises 3336, say whether the given pair of events are independent, mutually exclusive, or neither. A: Your first coin flip results in heads. B: Your second coin flip results in heads.37E38E39E40E41E42EIf a coin is tossed 11 times, find the probability of the sequence H, T, T, H, H, H, T, H, H, T, T. [HinT: See Example 5.]44EPersonal Bankruptcy In 2004 the probability that a person in the United States would declare personal bankruptcy was .006. The probability that a person in the United States would declare personal bankruptcy and had recently experienced a big three event (loss of job, medical problem, or divorce or separation) was .005.54 What was the probability that a person had recently experienced one of the big three events, given that she had declared personal bankruptcy? (Round your answer to one decimal place.)46EExisting Home Sales During the year ending April 30, 2015, there were approximately 5.0 million sales of existing homes in the United States, of which 1.2 million were sold in the West. During April 2015 there were a total of 450,000 existing homes sold in the United States, of which 110,000 were sold in the West.56 a. Find the probability that a home sale in the year ending April 30, 2015, took place in the West, given that the home was sold during April of that year. b. Find the probability that a home sale in the year ending April 30, 2015, took place in April of that year, given that it took place in the West.Existing Home Sales Refer to the data given in Exercise 47. a. Find the probability that a home sale in the year ending April 30, 2015, took place outside the West, given that the home was sold during April of that year. b. Find the probability that a home sale in the year ending April 30, 2015, took place in April of that year, given that it took place outside the West.49E50EMarketing A market survey shows that 40% of the population used Brand X laundry detergent last year, 5% of the population gave up doing its laundry last year, and 4% of the population used Brand X and then gave up doing laundry last year. Are the events of using Brand X and giving up doing laundry independent? Is a user of Brand X detergent more or less likely to give up doing laundry than a randomly chosen person?Marketing A market survey shows that 60% of the population used Brand Z computers last year, 5% of the population quit their jobs last year, and 3% of the population used Brand Z computers and then quit their jobs. Are the events of using Brand Z computers and quitting ones job independent? Is a user of Brand Z computers more or less likely to quit a job than a randomly chosen person?Road Safety In 1999 the probability that a randomly selected vehicle would be involved in a deadly tire-related accident was approximately 3106, whereas the probability that a tire-related accident would prove deadly was .02.59 What was the probability that a vehicle would be involved in a tire-related accident?54EPublishing Exercises 5562 are based on the following table, which shows the results of a survey of 100 authors by a publishing company: New Authors Established Authors Total Successful 5 25 30 Unsuccessful 15 55 70 Total 20 80 100 Compute the following conditional probabilities: An author is established, given that she is successful.56E57E58E59E60E61EPublishing Exercises 5562 are based on the following table, which shows the results of a survey of 100 authors by a publishing company: New Authors Established Authors Total Successful 5 25 30 Unsuccessful 15 55 70 Total 20 80 100 Compute the following conditional probabilities: An established author is successful.63EIn Exercises 6368, draw an appropriate tree diagram, and use the multiplication principle to calculate the probabilities of all the outcomes. [HinT: See Example 3.] Product Reliability You purchase Brand X memory chips one quarter of the time and Brand Y memory chips the rest of the time. Brand X memory chips have a 1% failure rate, while Brand Y memory chips have a 3% failure rate.In Exercises 6368, draw an appropriate tree diagram, and use the multiplication principle to calculate the probabilities of all the outcomes. [HinT: See Example 3.] Car Rentals Your auto rental company rents out 30 small cars, 24 luxury sedans, and 46 slightly damaged budget vehicles. The small cars break down 14% of the time, the luxury sedans break down 8% of the time, and the budget cars break down 40% of the time66E67E68EEducation and Employment Exercises 6978 are based on the following table, which shows U.S. employment figures for 2014, broken down by educational attainment.61 All numbers are in millions and represent civilians aged 25 years and over. Those classed as not in labor force were not employed nor actively seeking employment. Round all answers to two decimal places. Employed Unemployed Not in Labor Force Total Less Than High School Diploma 9.9 1.0 13.2 24.1 High School Diploma Only 33.9 2.2 25.9 62.0 Some College or Associates Degree 35.3 2.0 18.4 55.7 Bachelors Degree or Higher 48.8 1.6 16.9 67.3 Total 127.9 6.8 74.4 209.1 Find the probability that a person was employed, given that the person had a bachelors degree or higher.70E71E72E73E74E75E76E77E78E79E80E81E82EInternet Use in 2000 The following pie chart shows the percentage of the population that used the Internet in 2000, broken down further by family income and based on a survey taken in August 2000:64 a. Determine the probability that a randomly chosen person was an Internet user, given that his or her family income was at least $35,000. b. Based on the data, was a person more likely to be an Internet user if his or her family income was less than $35,000 or $35,000 or more? (Support your answer by citing the relevant conditional probabilities.)84E85E86E87E88E89E90E91E92E93E94E95E96EUltimate Hockey Cyber Video Games, Inc., the makers of Ultimate Hockey (see the discussion at the beginning of this section), switched to a cheaper ad agency whose TV ad had no effect whatsoever on sales according to a survey. Unfortunately, a student intern accidentally erased some of the survey data in the table below: Saw Ad Did Not See Ad Total Purchased Game 20 40 60 Did Not Purchase Game 180 ? ? Total 200 ? ? Calculate the missing quantities.98E99E100E101E102E103E104E105E106E107E108E109E110E111E112EIn Exercises 18, use Bayes theorem or a tree diagram to calculate the indicated probability. Round all answers to four decimal places. [HinT: See Quick Example 1 and Example 3.] P(A|B)=.8,P(B)=.2,P(A|B)=.3. Find P(B|A).2EIn Exercises 18, use Bayes theorem or a tree diagram to calculate the indicated probability. Round all answers to four decimal places. [HinT: See Quick Example 1 and Example 3.] P(X|Y)=.8,P(Y )=.3,P(X|Y)=.5. Find P(Y|X).4EIn Exercises 18, use Bayes theorem or a tree diagram to calculate the indicated probability. Round all answers to four decimal places. [HinT: See Quick Example 1 and Example 3.] Y1,Y2,Y3 form a partition of S. P(X|Y1)=.4, P(X|Y2)=.5,P(X|Y3)=.6,P(Y1)=.8, P(Y2)=.1. Find P(Y1|X).6EIn Exercises 18, use Bayes theorem or a tree diagram to calculate the indicated probability. Round all answers to four decimal places. [HinT: See Quick Example 1 and Example 3.] Y1,Y2,Y3 form a partition of S. P(X|Y1)=.4, P(X|Y2)=.5,P(X|Y3)=.6,P(Y1)=.8, P(Y2)=.1. Find P(Y2|X).8EMusic Downloading According to a study on the effect of music downloading on spending on music, 11% of all Internet users had decreased their spending on music.69 We estimate that 40% of all music fans used the Internet at the time of the study.70 If 20% of nonInternet users had decreased their spending on music, what percentage of those who had decreased their spending on music were Internet users? [HinT: See Examples 1 and 2.]10EWeather It snows in Greenland an average of once every 25 days, and when it does, glaciers have a 20% chance of growing. When it does not snow in Greenland, glaciers have only a 4% chance of growing. What is the probability that it is snowing in Greenland when glaciers are growing?12EUniversity Admissions In fall 2014, 34% of applicants with a Math SAT of 700 or more were admitted by the University of California, Los Angeles (UCLA), while 12% with a Math SAT of less than 700 were admitted. Further, 36% of all applicants had a Math SAT score of 700 or more.72 What percentage of admitted applicants had a Math SAT of 700 or more? (Round your answer to the nearest percentage point.)14ESide-Impact Hazard In 2004, 45.4% of all light vehicles were cars, and the rest were light trucks or SUVs. The probability that a severe side-impact crash would prove deadly to a driver depended on the type of vehicle he or she was driving at the time, as shown in the table:74 Car 1.0 Light Truck or SUV .3 What is the probability that the victim of a deadly side-impact accident was driving a car?16EAthletic Fitness Tests Any athlete who fails the Enormous State Universitys womens soccer fitness test is automatically dropped from the team. Last year, Mona Header failed the test but claimed that this was due to the early hour. (The fitness test is traditionally given at 5 am on a Sunday morning.) In fact, a study by the ESU Physical Education Department suggested that 50% of athletes fit enough to play on the team would fail the soccer test, although no unfit athlete could possibly pass the test. It also estimated that 45% of the athletes who take the test are fit enough to play soccer. Assuming that these estimates are correct, what is the probability that Mona was justifiably dropped?Academic Testing Professor Frank Nabarro insists that all senior physics majors take his notorious physics aptitude test. The test is so tough that anyone not going on to a career in physics has no hope of passing, whereas 60% of the seniors who do go on to a career in physics still fail the test. Further, 75% of all senior physics majors in fact go on to a career in physics. Assuming that you fail the test, what is the probability that you will not go on to a career in physics?Side-Impact Hazard (Compare Exercise 15.) In 2004, 27.3% of all light vehicles were light trucks, 27.3% were SUVs, and 45.4% were cars. The probability that a severe side-impact crash would prove deadly to a driver depended on the type of vehicle he or she was driving at the time, as shown in the table:76 Light Truck .210 SUV .371 Car 1.000 What is the probability that the victim of a deadly side-impact accident was driving an SUV? [HinT: See Example 3.]Side-Impact Hazard In 1986, 23.9% of all light vehicles were light trucks, 5.0% were SUVs, and 71.1% were cars. Refer to Exercise 19 for the probabilities that a severe side-impact crash would prove deadly. What is the probability that the victim of a deadly side-impact accident was driving a car? [HinT: See Example 3.]University Admissions In fall 2008, UCLA admitted 22% of its California resident applicants, 28% of its applicants from other U.S. states, and 22% of its international student applicants. Of all its applicants, 84% were California residents, 10% were from other U.S. states, and 6% were international students.77 What percentage of all admitted students were California residents? (Round your answer to the nearest 1%.)22EInternet Use (Historical) In 2000, 86% of all Caucasians in the United States, 77% of all African-Americans, 77% of all Hispanics, and 85% of residents not classified into one of these groups used the Internet for email.79 At that time, the U.S. population was 69% Caucasian, 12% African-American, and 13% Hispanic. What percentage of U.S. residents who used the Internet for email were Hispanic?24EMarket Surveys A New York Times survey of homeowners in the 1990s showed that 86% of those with swimming pools were married couples, and the other 14% were single.81 It also showed that 15% of all homeowners had pools. a. Assuming that 90% of all homeowners without pools are married couples, what percentage of homes owned by married couples have pools? b. Would it have been more profitable for pool manufacturers to go after single homeowners or married homeowners? Explain.26E27E28EEmployment in the 1980s In a 1987 survey of married couples with earnings, 95% of all husbands were employed. Of all employed husbands, 71% of their wives were also employed.83 Noting that either the husband or wife in a couple with earnings had to be employed, find the probability that the husband of an employed woman was also employed.30E31E32EBenefits of Exercise According to a study in The New England Journal of Medicine,86 202 of a sample of 5,990 middle-aged men had developed diabetes. It also found that men who were very active (burning about 3,500 calories daily) were half as likely to develop diabetes compared with men who were sedentary. Assume that one third of all middle-aged men are very active, and the rest are classified as sedentary. What is the probability that a middle-aged man with diabetes is very active?34E35E36E37E38E39E40E41E42E43E44EIn Exercises 110, write down the transition matrix associated with each state transition diagram.2E3EIn Exercises 110, write down the transition matrix associated with each state transition diagram.5E6E7E8EIn Exercises 110, write down the transition matrix associated with each state transition diagram.10E11E12E13E14E15E16E17E18E19E20E21E22E23E24E25E26E27E28E29E30E31E32E33E34EIn Exercises 2536, you are given a transition matrix P. Find the steady-state distribution vector. [HinT: See Example 4.] P=[.1.900100.2.8]36E37E38EPest Control In an experiment to test the effectiveness of the latest roach trap, the Roach Resort, 50 roaches were placed in the vicinity of the trap and left there for an hour. At the end of the hour, it was observed that 30 of the roaches had checked in, while the rest were still scurrying around. (Remember that once a roach checks in, it never checks out.) a. Set up the transition matrix P for the system with decimal entries, and calculate P2andP3. b. If a roach begins outside the Resort, what is the probability of its checking in by the end of 1 hour? 2 hours? 3 hours? c. What do you expect to be the long-term impact on the number of roaches? [HinT: See Example 5.]Employment You have worked for the Department of Administrative Affairs (DAA) for 27 years, and you still have little or no idea exactly what your job entails. To make your life a little more interesting, you have decided on the following course of action. Every Friday afternoon, you will use your desktop computer to generate a random digit from 0 to 9 (inclusive). If the digit is a zero, you will immediately quit your job, never to return. Otherwise, you will return to work the following Monday. a. Use the states (1) employed by the DAA and (2) not employed by the DAA to set up a transition probability matrix P with decimal entries, and calculate P2andP3. b. What is the probability that you will still be employed by the DAA after each of the next 3 weeks? c. What are your long-term prospects for employment at the DAA? [HinT: See Example 5.]Risk Analysis An auto insurance company classifies each motorist as high risk if the motorist has had at least one moving violation during the past calendar year and low risk if the motorist has had no violations during the past calendar year. According to the companys data, a high-risk motorist has a 50% chance of remaining in the high-risk category the next year and a 50% chance of moving to the low-risk category. A low-risk motorist has a 10% chance of moving to the high-risk category the next year and a 90% chance of remaining in the low-risk category. In the long term, what percentage of motorists fall in each category?42ETextbook Adoptions College instructors who adopt this book are (we hope!) twice as likely to continue to use the book the following semester as they are to drop it, whereas nonusers are nine times as likely to remain nonusers the following year as they are to adopt this book. a. Determine the probability that a nonuser will be a user in 2 years. b. In the long term, what proportion of college instructors will be users of this book?Confidence Level Tommy the Dunkers performance on the basketball court is influenced by his state of mind: If he scores, he is twice as likely to score on the next shot as he is to miss, whereas if he misses a shot, he is three times as likely to miss the next shot as he is to score. a. If Tommy has missed a shot, what is the probability that he will score two shots later? b. In the long term, what percentage of shots are successful?45E46E51E53E54E55E56E57E