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Understandable Statistics Concepts And Methods 13th Edition Charles Henry Brase, Corrinne Pellillo Brase - Solutions

Counting: Exam Answers There are five multiplechoice questions on an exam, each with four possible answers. Determine the number of possible answer sequences for the five questions. Only one of the sets can contain all five correct answers. If you are guessing, so that you are as likely to choose
Basic Computation Compute.(a) P7,2(b) C7,2(c) P3,3(d) C4,4 AppendixLO1
Combination: City Council There is money to send two of eight city council members to a conference in Honolulu. All want to go, so they decide to choose the members to go to the conference by a random process.How many different combinations of two council members can be selected from the eight who
Academic: Passing French Class records at Rockwood College indicate that a student selected at random has probability 0.77 of passing French 101. For the student who passes French 101, the probability is 0.90 that he or she will pass French 102. What is the probability that a student selected at
General: Two Dice In a game of craps, you roll two fair dice. Whether you win or lose depends on the sum of the numbers appearing on the tops of the dice. Let x be the random variable that represents the sum of the numbers on the tops of the dice.(a) What values can x take on?(b) What is the
Survey: Reaction to Poison Ivy Allergic reactions to poison ivy can be miserable. Plant oils cause the reaction. Researchers at Allergy Institute did a study to determine the effects of washing the oil off within 5 minutes of exposure. A random sample of 1000 people with known allergies to poison
General: Thumbtack Drop a thumbtack and observe how it lands.(a) Describe how you could use a relative frequency to estimate the probability that a thumbtack will land with its flat side down.(b) What is the sample space of outcomes for the thumbtack?(c) How would you make a probability assignment
Virus Transmission What are the chances of you catching a virus? The CDC estimated that on average 8% of the U.S. population gets sick with the flu virus every year. Suppose that the chance someone with the flu transmits it to another individual is 90%. If you were to meet a person at random, find
Salary Raise: Women Does it pay to ask for a raise? A national survey of heads of households showed the percentage of those who asked for a raise and the percentage who got one (USA Today).According to the survey, of the women interviewed, 24% had asked for a raise, and of those women who had asked
Critical Thinking For a class activity, your group has been assigned the task of generating a quiz question that requires use of the formula for conditional probability to compute P(B | A). Your group comes up with the following question: “If P(A and B) 5 0.40 and P(A) 5 0.20, what is the value
Critical Thinking You are given the information that P(A) 5 0.30 and P(B) 5 0.40.(a) Do you have enough information to compute P(A and B)? Explain.(b) If you know that events A and B are independent, do you have enough information to compute P(A and B)? Explain.AppendixLO1
Critical Thinking You are given the information that P(A) 5 0.30 and P(B) 5 0.40.(a) Do you have enough information to compute P(A or B)? Explain.(b) If you know that events A and B are mutually exclusive, do you have enough information to compute P(A or B)? Explain.AppendixLO1
Interpretation You are applying for two jobs, and you estimate the probability of getting an offer for the first job is 0.70 while the probability of getting an offer for the second job is 0.80. Assume the job offers are independent.(a) Compute the probability of getting offers for both jobs. How
Interpretation You are considering two facial cosmetic surgeries. These are elective surgeries and their outcomes are independent. The probability of success for each surgery is 0.90. What is the probability of success for both surgeries? If the probability of success for both surgeries is less
Statistical Literacy If two events A and B are independent, how do the probabilities P(A) and P(A | B) compare?AppendixLO1
Statistical Literacy If two events A and B are mutually exclusive, what is the value of P(A and B)?AppendixLO1
Statistical Literacy Consider the following two events for an individual:A 5owns a cell phone B 5owns a laptop computer Translate each event into words.(a) Ac(b) A and B(c) A or B(d) A | B(e) B | A AppendixLO1
Counting: Cellphone Passcodes The Viewpoint in this section, on page 172, describes the topic of cellphone passcodes used to prevent unwanted individuals from accessing your information. Each digit of the passcode must be a number from 0 to 9 where each digit can be repeated. Use the appropriate
Counting: Hiring The qualified applicant pool for six management trainee positions consists of seven women and five men.(a) How many different groups of applicants can be selected for the positions?(b) How many different groups of trainees would consist entirely of women?(c) Probability Extension
Counting: Grading One professor grades homework by randomly choosing 5 out of 12 homework problems to grade.(a) How many different groups of 5 problems can be chosen from the 12 problems?(b) Probability Extension Jerry did only 5 problems of one assignment. What is the probability that the problems
Counting: Hiring There are 15 qualified applicants for 5 trainee positions in a fast-food management program.How many different groups of trainees can be selected?AppendixLO1
Counting: Sales During the Computer Daze special promotion, a customer purchasing a computer and printer is given a choice of 3 free software packages.There are 10 different software packages from which to select. How many different groups of software packages can be selected?AppendixLO1
Counting: Sports The University of Montana ski team has five entrants in a men’s downhill ski event. The coach would like the first, second, and third places to go to the team members. In how many ways can the five team entrants achieve first, second, and third places?AppendixLO1
Counting: Lottery In the Cash Now lottery game there are 10 finalists who submitted entry tickets on time. From these 10 tickets, three grand prize winners will be drawn. The first prize is $1 million, the second prize is $100,000, and the third prize is $10,000.Determine the total number of
Counting: Hiring There are three nursing positions to be filled at Lilly Hospital. Position 1 is the day nursing supervisor; position 2 is the night nursing supervisor;and position 3 is the nursing coordinator position.There are 15 candidates qualified for all three of the positions. Determine the
Compute C8,8.AppendixLO1
Compute C7,7.AppendixLO1
Compute C8,3.AppendixLO1
Compute C5,2.AppendixLO1
Compute P9,9.AppendixLO1
Compute P7,7.AppendixLO1
Compute P8,3.AppendixLO1
Compute P5,2.AppendixLO1
Counting: Outcomes You toss a pair of dice.(a) Determine the number of possible pairs of outcomes. (Recall that there are six possible outcomes for each die.)(b) There are three even numbers on each die. How many outcomes are possible with even numbers appearing on each die?(c) Probability
Counting: Agriculture Barbara is a research biologist for Green Carpet Lawns. She is studying the effects of fertilizer type, temperature at time of application, and water treatment after application. She has four fertilizer types, three temperature zones, and three water treatments to test.
Multiplication Rule for Counting A sales representative must visit four cities: Omaha, Dallas, Wichita, and Oklahoma City. There are direct air connections between each of the cities. Use the multiplication rule of counting to determine the number of different choices the sales representative has
Multiplication Rule for Counting Four wires (red, green, blue, and yellow) need to be attached to a circuit board. A robotic device will attach the wires. The wires can be attached in any order, and the production manager wishes to determine which order would be fastest for the robot to use. Use
Tree Diagram(a) Make a tree diagram to show all the possible sequences of answers for three multiple-choice questions, each with four possible responses.(b) Probability Extension Assuming that you are guessing the answers so that all outcomes listed in the tree are equally likely, what is the
Tree Diagram There are six balls in an urn. They are identical except for color. Two are red, three are blue, and one is yellow. You are to draw a ball from the urn, note its color, and set it aside. Then you are to draw another ball from the urn and note its color.(a) Make a tree diagram to show
Tree Diagram(a) Draw a tree diagram to display all the possible outcomes that can occur when you flip a coin and then toss a die.(b) How many outcomes contain a heads and a number greater than 4?(c) Probability Extension Assuming the outcomes displayed in the tree diagram are all equally likely,
Tree Diagram(a) Draw a tree diagram to display all the possible heads–tails sequences that can occur when you flip a coin three times.(b) How many sequences contain exactly two heads?(c) Probability Extension Assuming the sequences are all equally likely, what is the probability that you will get
Critical Thinking You need to know the number of different arrangements possible for five distinct letters.You decide to use the permutations rule, but your friend tells you to use 5!. Who is correct? Explain.AppendixLO1
Critical Thinking For each of the following situations, explain why the combinations rule or the permutations rule should be used.(a) Determine the number of different groups of 5 items that can be selected from 12 distinct items.(b) Determine the number of different arrangements of 5 items that
Statistical Literacy Consider the following scenarios and determine whether to use the permutation rule or combination rule to count the total number of outcomes.(a) Choosing three flavors of ice cream from a selection of 20 different choices.(b) Electing the president, vice-president, and
Statistical Literacy Consider a series of events.How does a tree diagram help you list all the possible outcomes of a series of events? How can you use a tree diagram to determine the total number of outcomes of a series of events?AppendixLO1
Statistical Literacy What is the main difference between a situation in which the use of the permutations rule is appropriate and one in which the use of the combinations rule is appropriate?AppendixLO1
Explain how counting techniques relate to probability in everyday life.AppendixLO1
Compute the number of (nonordered) groupings of outcomes using combinations.AppendixLO1
Compute the number of ordered arrangements of outcomes using permutations.AppendixLO1
Organize outcomes in a sample space using tree diagrams.AppendixLO1
Brain Teaser The Reverend Thomas Bayes (1702–1761) was an English mathematician who discovered an important rule of probability (see Bayes’s theorem, Appendix I, part I). A key feature of Bayes’s theorem is the formula P(B) 5P(B | A) ? P(A) 1P(B | Ac ) ? P(Ac )Explain why this formula is
P(A | B) 1P(Ac | B) 51 AppendixLO1
If A and B are mutually exclusive, then P(A | B) 5 0.AppendixLO1
If A and B are both mutually exclusive and independent, then at least one of P(A) or P(B) must be zero.AppendixLO1
If A and B are mutually exclusive, they must also be independent.AppendixLO1
If A and B are independent events, they must also be mutually exclusive events.AppendixLO1
P(Ac or Bc )  2 2P(A) 2P(B)AppendixLO1
P(Ac and Bc )  12P(A)AppendixLO1
P(A | B) . P(A) if A and B are independent events AppendixLO1
P(A and B)  P(A)AppendixLO1
P(A or B) $ P(A) if A and B are independent events AppendixLO1
P(A | B) $ P(A and B)AppendixLO1
P(A or B) 5P(A) 1P(B)AppendixLO1
P(A | Ac ) 51 AppendixLO1
P(A or Ac ) 5 0 AppendixLO1
P(A and Ac ) 5 0 AppendixLO1
Olympics: Steroid Testing. Use of performance enhancing drugs in the Olympics have always been frowned upon and has led to many participants being either disqualified or banned from participating in athletic competitions. Suppose that a steroid test was conducted prior to the 2020 Olympics to
Medical: Tuberculosis The state medical school has discovered a new test for tuberculosis. (If the test indicates a person has tuberculosis, the test is positive.) Experimentation has shown that the probability of a positive test is 0.82, given that a person has tuberculosis. The probability is
Education: College of Nursing At Litchfield College of Nursing, 85% of incoming freshmen nursing students are female and 15% are male. Recent records indicate that 70% of the entering female students will graduate with a BSN degree, while 90% of the male students will obtain a BSN degree. If an
Franchise Stores: Profits Wing Foot is a shoe franchise commonly found in shopping centers across the United States. Wing Foot knows that its stores will not show a profit unless they gross over$940,000 per year. Let A be the event that a new Wing Foot store grosses over $940,000 its first year.Let
Survey: Customer Loyalty Are customers more loyal in the east or in the west? The following table is based on information from Trends in the United States, published by the Food Marketing Institute, Washington, D.C. The columns represent length of customer loyalty (in years) at a primary
Survey: Lung/Heart In an article titled “Diagnostic accuracy of fever as a measure of postoperative pulmonary complications” (Heart Lung, Vol. 10, No. 1, p. 61), J. Roberts and colleagues discuss using a fever of 388C or higher as a diagnostic indicator of postoperative atelectasis (collapse of
Survey: Medical Tests Diagnostic tests of medical conditions can have several types of results. The test result can be positive or negative, whether or not a patient has the condition. A positive test (+) indicates that the patient has the condition. A negative test (−) indicates that the patient
Survey: Sales Approach In a sales effectiveness seminar, a group of sales representatives tried two approaches to selling a customer a new automobile:the aggressive approach and the passive approach. For 1160 customers, the following record was kept:Sale No Sale Row Total Aggressive 270 310 580
Focus Problem: Expand Your Knowledge This problem continues the Focus Problem. The solution involves applying several basic probability rules and a little algebra to solve an equation.(a) If the polygraph of Problem 32 indicated that 30% of the questions were answered with lies, what would you
Focus Problem: Lie Detector Test In this problem, you are asked to solve part of the Focus Problem at the beginning of this chapter. In his book Chances:Risk and Odds in Everyday Life, James Burke says that there is a 72% chance a polygraph test (lie detector test) will catch a person who is, in
Health Care: Flu Based on data from the Statistical Abstract of the United States, 112th edition, only about 14% of senior citizens (65 years old or older) get the flu each year. However, about 24% of the people under 65 years old get the flu each year. In the general population, there are 12 5. %
Marketing: Toys USA Today gave the information shown in the table about ages of children receiving toys. The percentages represent all toys sold.Age (years) Percentage of Toys 2 and under 15%3–5 22%6–9 27%10–12 14%13 and over 22%What is the probability that a toy is purchased for someone(a) 6
General: Deck of Cards You draw two cards from a standard deck of 52 cards, but before you draw the second card, you put the first one back and reshuffle the deck.(a) Are the outcomes on the two cards independent?Why?(b) Find P(3 on 1st card and 10 on 2nd).(c) Find P(10 on 1st card and 3 on
General: Deck of Cards You draw two cards from a standard deck of 52 cards, but before you draw the second card, you put the first one back and reshuffle the deck.(a) Are the outcomes on the two cards independent? Why?(b) Find P(Ace on 1st card and King on 2nd).(c) Find P(King on 1st card and Ace
General: Deck of Cards You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second.(a) Are the outcomes on the two cards independent?Why?(b) Find P(3 on 1st card and 10 on 2nd).(c) Find P(10 on 1st card and 3 on 2nd).(d) Find the probability of
General: Deck of Cards You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second.(a) Are the outcomes on the two cards independent?Why?(b) Find P(Ace on 1st card and King on 2nd).(c) Find P(King on 1st card and Ace on 2nd).(d) Find the probability
General: Roll Two Dice You roll two fair dice, a green one and a red one.(a) What is the probability of getting a sum of 7?(b) What is the probability of getting a sum of 11?(c) What is the probability of getting a sum of 7 or 11?Are these outcomes mutually exclusive?Problems 26–29 involve a
General: Roll Two Dice You roll two fair dice, a green one and a red one.(a) What is the probability of getting a sum of 6?(b) What is the probability of getting a sum of 4?(c) What is the probability of getting a sum of 6 or 4?Are these outcomes mutually exclusive?AppendixLO1
General: Roll Two Dice You roll two fair dice, a green one and a red one.(a) Are the outcomes on the dice independent?(b) Find P(1 on green die and 2 on red die) .(c) Find P(2 on green die and 1 on red die).(d) Find P[(1 on green die and 2 on red die) or (2 on green die and 1 on red
General: Roll Two Dice You roll two fair dice, a green one and a red one.(a) Are the outcomes on the dice independent?(b) Find P(5 on green die and 3 on red die).(c) Find P(3 on green die and 5 on red die).(d) Find P[(5 on green die and 3 on red die) or (3 on green die and 5 on red die)].AppendixLO1
Environmental: Land Formations Arches National Park is located in southern Utah. The park is famous for its beautiful desert landscape and its many natural sandstone arches. Park Ranger Edward McCarrick started an inventory (not yet complete) of natural arches within the park that have an opening
General: Candy Colors M&M plain candies come in various colors. The distribution of colors for plain M&M candies in a custom bag is Color Purple Yellow Red Orange Green Blue Brown Percentage 20% 20% 20% 10% 10% 10% 10%Suppose you have a large custom bag of plain M&M candies and you choose one candy
Critical Thinking Consider the following events for a person selected at random from the general population A 5person has a college degree B 5person is employed by a large corporation Translate each of the symbols into phrases using the given context.(a) P(A and B)(b) P(A or B)(c) P(A | B)(d) P(B |
Critical Thinking Consider the following events for a person selected at random from the general population A 5person watches YouTube daily B 5person is under the age of 25 Translate each of the symbols into phrases using the given context.(a) P(A and B)(b) P(A or B)(c) P(A | B)(d) P(B |
Critical Thinking Consider the following events for a college student selected at random:A B5 5student is female student is majoring in business Translate each of the following phrases into symbols.(a) The probability the student is male or is majoring in business(b) The probability a female
Critical Thinking Consider the following events for a driver selected at random from the general population:A B5 5driver is under 25 years old driver has received a speeding ticket Translate each of the following phrases into symbols.(a) The probability the driver has received a speeding ticket and
Critical Thinking Suppose two events A and B are independent, with P(A) 0 and P(B) 0. By working through the following steps, you’ll see why two independent events are not mutually exclusive.(a) What formula is used to compute P(A and B)? Is P(A and B) 0? Explain.(b) Using the information
Critical Thinking Suppose two events A and B are mutually exclusive, with P(A) 0 and P(B) 0. By working through the following steps, you’ll see why two mutually exclusive events are not independent.(a) For mutually exclusive events, can event A occur if event B has occurred? What is the value
Critical Thinking Milo made up another question for a small quiz. He assigns the probabilities P(A) 5 0.6, P(B) 5 0.7, P(A | B) 5 0.1 and asks for the probability P(A or B). What is wrong with the probability assignments?AppendixLO1
Critical Thinking Blake is making up questions for a small quiz on probability. They assign these probabilities: P(A) 5 0.3, P(B) 5 0.3, P(A and B) 5 0.4. What is wrong with these probability assignments?AppendixLO1
Basic Computation: Rules of Probability Given P(Ac ) 5 0.8, P(B) 5 0.3, P(B | A) 5 0.2:(a) Compute P(A and B).(b) Compute P(A or B)AppendixLO1
Basic Computations: Rules of Probability Given P(A) 5 0.2, P(B) 5 0.5, P(A | B) 5 0.3:(a) Compute P(A and B).(b) Compute P(A or B).AppendixLO1
Basic Computation: Multiplication Rule Given P(A) 5 0.7 and P(B) 5 0.8:(a) If A and B are independent events, compute P(A and B).(b) If P(B | A) 5 0.9, compute P(A and B).AppendixLO1
Basic Computation: Multiplication Rule Given P(A) 5 0.2 and P(B) 5 0.4:(a) If A and B are independent events, compute P(A and B).(b) If P(A | B) 5 0.1, compute P(A and B).AppendixLO1

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