Question: For two events A and B, the

> A file cabinet has 8 student folders arranged alphabetically according to last name. Three files are selected at random. (a) How many different selections are possible? (b) Find the probability that the selected folders are all adjacent.

> If there are too many leaves on some stems in a stem-and-leaf display, we might double the number of stems. The leaves 0- 4 could hang on one stem and 5- 9 on the repeated stem. For the observations. We would get the double-stem display Construct a doubl

> A box of tulip bulbs contains six bulbs that produce yellow flowers and five bulbs that produce red flowers. Four bulbs are to be randomly selected without replacement. Find the probability that: (a) Exactly two of the select ed bulbs produce red flower

> Refer to Exercise 4.91, and further suppose that the 5 respondents who are below 30 consist of 2 males and 3 females, whereas those above 30 consist of 4 males and 2 females. Now, the researcher wants to randomly select 2 males and 2 females to be assign

> An advertisement seeking volunteers for a clinical research draws 11 respondents. Of these respondents, 5 are below age 30 and 6 are over 30. The researcher will randomly select 4 persons to assign to a particular treatment regimen. (a) How many selecti

> Are the following methods of selection likely to produce a random sample of 5 students from your school? Explain. (a) Pick 5 students throwing flying discs on the mall. (b) Pick 5 students who are studying in the library on Friday night. (c) Select 5

> There are four elementary outcomes in a sample space. If P(e1) = .3, P(e2) = .4, and P(e3) = .2, what is the probability of e4?

> In one area city park, there are 15 trees, of which 9 are bushy and 6 that are not bushy. If 5 trees are selected at random to receive a new spray, what is the probability that exactly 3 bushy trees are selected?

> Nine agricultural plots for an experiment are laid out in a square grid as shown. Three plots are to be selected at random . (a) Find the probability that all 3 are in the same row. (b) Find the probability that all 3 are in different rows.

> A college senior is selected at random from each state. Next, one senior is selected at random from the group of 50. Does this procedure produce a senior selected at random from those in the United States?

> Refer to Exercise 4.85. Suppose the sampling of 3 alternators is done by randomly choosing one after another and without replacement. The event A can then be described as G 1 G2G3, where G denotes "good" and the suffixes refer to the order of the draws.

> A batch of 18 used automobile alternators contains 4 defectives. If 3 alternators are sampled at random, find the probability of the event (a) A = [ None of the defectives appear] (b) B = [ Exactly two defectives appear ]

> The following is a stem-and-leaf display with two-digit leaves. (The leading leaf digit = 10.0.) List the corresponding measurements.

> A local company is giving away five streaming devices to persons who visit its website and register on a specified day. Each person is allowed to register three times for the drawing. If, at the time of drawing, there are 6200 entries, what is the probab

> After a preliminary screening, the list of qualified jurors consists of 10 males and 7 females. The 5 jurors the judge selects from this list are all males. Did the selection process seem to discriminate against females? Answer this by computing the prob

> Out of 12 people applying for an assembly job, 3 cannot do the work. Suppose two persons will be hired . (a) How many distinct p airs are possible? (b) In how many of the pairs will O or 1 person not be able to do the work? (c) If two persons are chos

> A psych ologist will select 5 preschool children from a class of 11 students in order to try out new abuse awareness material. (a) How many different selections are possible? (b) Suppose 4 of the 11 children are males. If the 5 selected children were t

> If a coin is tossed 11 times, the outcome can be recorded as an 11-character sequence of H's and T's according to the results of the successive tosses. In h ow m any ways can there be 4 H's and 7 T's? (Put differently, in how many ways can one choose 4 p

> Consider the following experiment: A coin will be tossed twice. If both tosses show heads, the experiment will stop. If one head is obtained in the two tosses, the coin will be tossed one more time, and in the case of both tails in the two tosses, the co

> Of 10 available candidates for membership in a university committee, 6 are men and 4 are women. The committee is to consist of 4 persons. (a) How many different selections of the committee are possible? (b) H ow many selections are possible if the comm

> Evaluate: (a) (8 4) (b) (10 3) (c) (21 2) (d) (21 19) (e) (25 3) (f) (25 22)

> Refer to Example where a manufacturer had difficulty getting enough LED screens. Now suppose, because of the shortage, the manufacturer had to obtain 30% of the screens from the second supplier and 15% from the third supplier. Find the (a) Probability

> A cable TV provider assigns 80% of its service calls to an independent contractor and 9% of these calls result in consumer complaints. The other 20% of the service calls are made by the companies' own employees, and these result in a 4% complaint rate. F

> A federal government study of the oil reserves in Elk Hills, CA, included a study of the amount of iron present in the oil. Make a stem-and-leaf display.

> At one automated international airport arrival location, facial identification software compares a camera image of the traveler with a scan of their passport picture. The procedure correctly concludes a match with 99.4% of males and 98.8% of females. The

> Refer to Example concerning spam but now suppose that a new list is available. Among the 1000 messages, the 350 spam messages have 310 that contain words on this list and the 650 normal messages have 70 that contain words on the list. (a) Obtain the pro

> In a county, men constitute 60% of the labor force. The rates of unemployment are 5.1 % and 4.3% among males and females, respectively. (a) In the context, of selecting a worker at random from the country labor force, state what probabilities the forego

> Carol and Karl both solve difficult computer problems that come to the student desk. Carol makes 60% of the repairs and Karl 40%. However, Carol's repairs are incomplete 4% of the time and Karl's are incomplete 6% of the time. (a) Determine the probabil

> Repeat Example 20 but change P(A I B) to .03. Data from Example 20: A is the event that a person tests positive for a serious virus and B is the event that the person actually has the virus. Suppose a person tests positive. Use Bayes' Theorem to update

> Consider tossing two fair coins and the events A: Head in the first toss B: Head in the second toss C: Both heads or both tails in the two tosses (a) Verify that the property of independence holds for all event pairs. (b) Show that P (ABC) is different f

> Bob, John, Linda, and Sue are the finalists in the campus bowling tournament. The winner and the first runner-up will be sent to a statewide competition. (a) List the sample space concerning the outcomes of the local tournament. (b) Give the compositio

> Of the patients reporting to a clinic with the symptoms of sore throat and fever, 25% have strep throat, 40% have an allergy, and 10% have both. (a) What is the probability that a patient selected at random has strep throat, an allergy, or both? (b) Are

> Refer to Exercise 4.48. Given that a landfill selected at random is found to have a high concentration of mercury, what is the probability that its concentration is: (a) High in barium? (b) Low in both arsenic and barium? ( c) High in either arsenic or b

> In 80% of the cases an electronic scanner is successful in detecting flaws in a material specimen. Three material specimens containing flaws will be tested with the scanner. Assume that the tests are independent. (a) List the sample space and assign pro

> The following data represent the scores of 40 students on a college qualification test (courtesy of R. W. Johnson). Make a stem-and-leaf display.

> An accountant screens large batches of bills according to the following sampling inspection plan. She inspects 4 bills chosen at random from each batch and p asses the batch if, among the 4, none is irregular. Find the probability that a batch will be pa

> Approximately 40% of the Wisconsin population have type 0 blood. If 4 persons are selected at random to be donors, find P [ at least one type O ] .

> Of three events, A, B, and C, suppose events A and B are independent and events B and C are mutually exclusive. Their probabilities are P(A) = .6, P(B) = .3, and P( C ) = .2. Express the following events in set notation and calculate their probabilities.

> A restaurant critic goes to a place twice. If she has an unsatisfactory experience during both visits, she will go once more. Otherwise she will make only the two visits. Assuming that the results for different visits are independent and that the probabi

> Of 20 rats in a cage, 12 are males and 9 are infected with a virus that causes hemorrhagic fever. Of the 12 male rats, 7 are infected with the virus. One rat is randomly selected from the cage. (a) If the selected rat is found to be infected, what is the

> Refer to Exercise 4.45. (a) If a fast food restaurant selected at random is found to comply with safety standards, what is the probability that it violates sanitary standards? (b) If a restaurant selected at random is found to violate at least one of t

> Suppose P(A) = .6andP(B) = .22. (a) Determine P ( A U B ) if A and B are independent. (b) Determine P ( A U B) if A and B are mutually exclusive. (c) Find P ( A I B) if A and B are mutually exclusive.

> When bidding on two projects, the president and vice president of a construction company make the following probability assessments for winning the contracts. For both cases, examine whether or not the probability assignment is permissible.

> If the probability of running out of gas is .03 and the probability the electronic starting system will not work is .01, (a) What is the probability that there will be enough gas and that the starting system will work? Assume the two events are independ

> An insurance company's records of 12,299 automobile insurance policies revealed that 2073 made a claim. Among insured drivers under age 25, there were 1032 claims out of 5192 policies (courtesy of J. Hickman). Assuming the claim history is valid for the

> Referring to Exercise 2.20, construct a density histogram using the intervals (6.5, 6.7], (6.7, 6.9], (6.9, 7.1], (7.1, 7.5], and (7.5, 7.9]. Using R: With the observations in x hist(x,breaks= c(6.5,6. 7,6.9, 7.1, 7.5, 7 .9),prob=T) Data from Exercise 2

> One type of passenger airplane has four engines but it can still fly with only one. Suppose each engine has probability .002 of failing during a flight. (a) Calculate the probability of all four engines failing during the same flight. Assume independenc

> An urn contains two green balls and three red balls. Suppose two balls will be drawn at random one after another and without replacement (i.e., the first ball drawn is not returned to the urn before the second one is drawn). (a) Find the probabilities o

> Records of student patients at a dentist's office concerning fear of visiting the dentist suggest the following proportions. For a student selected at random, consider the events A = [ Fear ] M = [ Middle school ] (a) Find the probabilities P(A) P(AM

> A witness identified a suspect as having blond hair. However, when tested under lighting conditions similar to those on the night of the incident, it was concluded that the probability of correctly identifying blond h air is .80 and the probability of be

> Th e following data relate to the proportions in a population of drivers. A = Defensive driver training last year B = Accident in current year The probabilities are given in the accompanying Venn diagram. Find P( B I A ). Are A and B independent?

> Refer to Exercise 4.39. Find (a) The conditional probability that B occurs given that A occurs. (b) The conditional probability that B does not occur given that A occurs. (c) The conditional prob ability that B occurs given that A does not occur. Dat

> A person is randomly selected from persons working in your state. Consider the two events A = [Lawyer] B = [ Driving a new luxury car ] Given that the person selected drives a new luxury car, would you expect the probability of A to be larger, the same,

> Identify these events in Exercise 4.4. (a) Not more than one correct identification. (b) Less accidents than last year. (c) Longer than the 90-day warranty but less than 425.4 days. Data from Exercise 4.4: Construct a sample space for each of the fol

> A person is randomly selected from persons working in your state. Consider the two events A = [ Earned over $70,000 last year] B = [ College graduate ] Given that the person is a college graduate, would you expect the probability of A to be larger, th

> In a recent year, 35 sites around the world experienced earthquakes of magnitude greater than 6.5. Construct a histogram using equal-length intervals starting with (6.5, 6.8], where the right-hand endpoint is included but not the left-hand endpoint.

> A social networking site reported the number of passwords memorized by 150 visitors who agreed to participate. Identify the statistical population and the sample for the number of passwords memorized.

> The following frequency table shows the classification of 58 landfills in a state according to their concentration of the three hazardous chemicals arsenic, barium, and mercury. If a landfill is selected at random, find the probability that it has: (a)

> The medical records of the male diabetic patients reporting to a clinic during one year provide the following percentages. Suppose a patient is chosen at random from this group, and the events A , B, and C are defined as follows. A = [ He has a serious c

> Given that the probability that A occurs is .3, the probability that B does not occur is .6, and the probability that either A or B occurs is .5, find: (a) The probability that A does not occur. (b) The probability that both A and B occur. (c) The pro

> Of 18 fast food restaurants in a city, 7 are in violation of sanitary standards, 8 are in violation of safety standards, and 4 are in violation of both. If a fast food restaurant is chosen at random, what is the probability that it is in compliance with

> In a class of 32 seniors and graduate students, 20 are men and 12 are graduate students of whom 8 are women . If a student is randomly selected from this class, what is the probability that the selected student is (a) a senior7 (b) a male graduate studen

> From the probabilities shown in this Venn diagram, determine the probabilities of the following events. (a) A does not occur. (b) A occurs and B does not occur. (c) Exactly one of the events A and B occurs.

> If P(A) = .4 and P(B) = .7, can A and B be mutually exclusive? Why or why not ?

> Binge drinking for males is consuming 5 drinks in two hours and for females it is consuming 4 drinks. Consider the two events A = [ Binge drinking ] B = [Female ] A recent survey by the National Center for Health Statistics suggests the probabilities

> Refer to Exercise 4.39. Express the following events in set notation and find their probabilities. (a) B occurs and A does not occur. (b) N either A nor B occurs. (c) Either A occurs or B does not occur. Data from Exercise 4.39: Consider the two even

> Construct a sample space for each of the following experiments. (a) Someone claims to be able to taste the difference between the same brand of bottled, tap, and canned draft beer. A glass of each is poured and given to the subject in an unknown order.

> A zoologist collected wild lizards in the Southwestern United States. Thirty lizards from the genus Phrynosoma were placed on a treadmill and their speed measured. The recorded speed (meters/second) is the fastest time to run a half meter (courtesy of K.

> Consider the two events. A = [Obese] B = [Male] for persons in the age group 20-39 years old. A recent survey by the National Center for Health Statistics suggests the probabilities P(A) = .36 P(B) = .50 P(AB) = .18 for a randomly selected person. (a

> Refer to Exercise 4.31. Suppose the elementary outcomes are assigned these probabilities. (a) Find P(A), P(B),and P(AB). (b) Employing the laws of probability and the results of part (a), calculate P(A¯) and P( A U B). (c) Verify your answe

> A sample space consists of 9 elementary outcomes e1, e2 , … , e9 whose probabilities are Suppose (a) Calculate P(A), P(B), and P(AB). (b) Using the addition law of probability, calculate P( A U B). (c) List the composition of the ev

> For the experiment of Exercise 4.35, give a verbal description of each of the following events and also state the composition of the event. (a) C¯ (b) CA (c) A U C¯ Data from Exercise 4.35: Four applicants are interviewed for an administrative position

> Four applicants are interviewed for an administrative position with an environmental lobby. They have the following characteristics. 1. Psychology major, male, GPA 3 .5 2. Chemistry major, fem ale, GPA 3.3 3. Journalism major, female, GPA 3.7 4. Mathemat

> Suppose you have h ad interviews for summer jobs at a grocery store, a discount store, and a movie theater. Let G, D, and M denote the events of your getting an offer from the grocery store, the discount store, and the movie theater, respectively. Expres

> Refer to Exercise 4.32. Corresponding to each verbal description given here, write the event in set notation, give its composition, and find its probability. (a) C does not occur. (b) Both A and B occur. (c) A occurs and B does not occur. (d) Neither

> A sample space consists of 8 elementary outcomes with the following probabilities. P(e1) = .07 P(e2) = P(e3) = P(e4) = .11 P(e5) = P (e6) = P (e7) = P (e8) = .15 Three events are given as A { e1, e2 , e6 , e7 }, B { e2, e3, e7 ), and C = {e6 , e8). (a)

> Next week, a student worker will be assigned one morning of kitchen duty. The sample space has seven elementary outcomes e1 , e2, .. , e7 where e1 represents Sunday, e2 Monday, and so on. Two events are given as A = {e4 , e5, e6 , e7) and B = {e1, e6 , e

> Refer to Exercise 4.24. Using relative frequencies to estimate probabilities, find which 3 consecutive months have the lowest probability of a new birth. Data from Exercise 4.24: (a) Consider the simplistic model that human births are evenly distributed

> Tornadoes kill many people every year in the United States. The yearly number of lives lost during the 50 years 1962 through 2011 are summarized in the following table. (a) Calculate the relative frequency for the intervals [0, 25), [25, 50) and so on wh

> Identify the statement that best describes each P (A). (a) P(A) = .04 (i) P(A) is incorrect. (b) P(A) = .36 (ii)A rarely occurs. (c) P(A) = -.5 (iii) A occurs moderately often.

> Refer to Exercise 4.28. (a) Assign probabilities to the elementary outcomes. (b) Find P (A) and P (B) . Data from Exercise 4.28: A local bookstore intended to award three gift certificates in the amounts $100, $50, and $25 to the first, second, and th

> A local bookstore intended to award three gift certificates in the amounts $100, $50, and $25 to the first, second, and third customer to identify a mystery author. Unfortunately, a careless clerk in charge of mailing forgot the order and just randomly p

> A random selection of 1000 smartphone owners, ages 18-24 years old, were asked if they constantly check and use their phone. A total of 518 responded yes. (a) Estimate the probability that, a smartphone owner in that age group constantly checks or uses

> A plant geneticist crosses two parent strains, each with gene pairs of type aA. An offspring receives one gene from each parent. (a) Construct the sample space for the genetic type of the offspring. (b) Assign probabilities assuming that the selection o

> A government agency will randomly select one of the 14 paper mills in a state to investigate its compliance with federal safety standards. Suppose, unknown to the agency, 9 of these mills are in compliance, 3 are borderline cases, and 2 are in gross viol

> (a) Consider the simplistic model that human births are evenly distributed over the 12 calendar months. If a person is randomly selected, say, from a phone directory, what is the probability that his or her birthday would be in November or December? (b)

> Campers arriving at a summer camp will be asked one after another whether they have protection against Lyme disease M or not (N). The inspection will continue until one camper is found to be not protected or until five campers are checked, whichever occu

> Friends will be called, one after another, and asked to go on a weekend trip with you. You will call until one agrees to go (A) or four friends are asked, whichever occurs first. List the sample space for the number of calls.

> Fifteen persons reporting to a Red Cross center one day are typed for blood, and the following counts are found: If one person is randomly selected, what is the probability that this person's blood group is: (a) AB? (b) Either A or B? (c) Not O?

> According to the cause-and-effect diagram, where are the possible delays on the first floor?

> Birth rates in the 50 states, collected in a recent year by the Center for Health Statistics, are grouped into the following frequency table. Endpoint convention: Lower endpoint is included, upper endpoint is not. If one state is selected at random, what

> For each numerical value assigned to the probability of an event, identify the verbal statements that are appropriate. (a) 1.1 (b) 1/1.1 (c) 1/2 (d) 43/47 (e) 1/89 (f) 1.0 Verbal statements: (i) cannot be a probability, (ii) the event is very unlikely to

> A white and a colored die are tossed. The possible outcomes are shown in the illustration below. (a) Identify the events A = [ Sum = 6 ], B = [ Sum = 7], C = [ Sum is even ], D = [ Same number on each die ]. (b) If both die are "fair," assign probabilit

> Suppose you are eating at a pizza parlor with two friends. You have agreed to the following rule to decide who will pay the bill. Each person will toss a coin. The person who gets a result that is different from the other two will pay the bill. If all th

> A stack contains eight tickets numbered 1, 1, 2, 2, 2, 3, 3, 3 . One ticket will be drawn at random and its number will be noted. (a) List the sample space and assign probabilities to the elementary outcomes. (b) What is the probability of drawing an od

> A letter is chosen at random from the word "CHEERFUL." What is the probability that it is a vowel?

> Consider the experiment of tossing a fair coin three times. (a) List the sample space by drawing a tree diagram. (b) Assign probabilities to the elementary outcomes. (c) Find the probability of getting exactly one head.

> Among 41, 131 turkey permit holders for a recent hunting season in Wisconsin, 8845 harvested a bird. Assuming conditions are the same today, estimate the prob ability that a turkey will be harvested for a single permit.

> Refer to the day of birth data. Assuming conditions are the same today, estimate the probability that a baby will be born during a weekday. That is, not on Saturday or Sunday.

> The probability of an event is often expressed in terms of odds. Specifically, when we say that the odds are k to m that an event will occur, we mean that the probability of the event is k / ( k + m). For instance, "the odds are 4 to 1 that candidate Jon