4P4
> A baseball team consists of three outfielders, four infielders, a pitcher, and a catcher. Assuming that the outfielders and infielders are indistinguishable, how many batting orders are possible?
> A golf-course architect has four linden trees, five white birch trees, and two bald cypress trees to plant in a row along a fairway. In how many ways can the landscaper plant the trees in a row, assuming that the trees are evenly spaced?
> How many distinguishable DNA sequences can be formed using one A, four Cs, three Gs, and four Ts?
> How many distinguishable DNA sequences can be formed using three As, two Cs, two Gs, and three Ts?
> A family has eight children. If this family has exactly three boys, how many different birth and gender orders are possible?
> A family has six children. If this family has exactly two boys, how many different birth and gender orders are possible?
> How many different simple random samples of size 7 can be obtained from a population whose size is 100?
> How many different simple random samples of size 5 can be obtained from a population whose size is 50?
> To complete the Citizenship in the World merit badge, one must select two of the following seven organizations and describe their role in the world. Source: Boy Scouts of America 1. The United Nations 2. The World Court 3. World Organization of the Scout
> In the U.S. Senate, there are 21 members on the Committee on Banking, Housing, and Urban Affairs. Nine of these 21 members are selected to be on the Subcommittee on Economic Policy. How many different committee structures are possible for this subcomm
> A lottery exists where balls numbered 1–25 are placed in an urn. To win, you must match the four balls chosen in the correct order. How many possible outcomes are there for this game?
> Four members from a 50-person committee are to be selected randomly to serve as chairperson, vice-chairperson, secretary, and treasurer. The first person selected is the chairperson; the second, the vice-chairperson; the third, the secretary; and the fou
> Four members from a 20-person committee are to be selected randomly to serve as chairperson, vice-chairperson, secretary, and treasurer. The first person selected is the chairperson; the second, the vice-chairperson; the third, the secretary; and the fou
> In how many ways can the top 2 horses finish in a 10-horse race?
> Suppose 40 cars start at the Indianapolis 500. In how many ways can the top 3 cars finish the race?
> How many different license plate numbers can be made by using one letter followed by five digits selected from the digits 0 through 9?
> A combination lock has 50 numbers on it. To open it, you turn counterclockwise to a number, then rotate clockwise to a second number, and then counterclockwise to the third number. Repetitions are allowed. (a) How many different lock combinations are the
> How many user names are possible in Problem 41 if the last character must be a digit?
> Suppose that a local area network requires eight letters for user names. Lower- and uppercase letters are considered the same. How many user names are possible for the local area network?
> A student entering a doctoral program in educational psychology is required to select two courses from the list of courses provided as part of his or her program. EPR 616, Research in Child Development EPR 630, Educational Research Planning and Interpret
> A Social Security number is used to identify each resident of the United States uniquely. The number is of the form xxx–xx–xxxx, where each x is a digit from 0 to 9. (a) How many Social Security numbers can be formed? (b) What is the probability of corre
> Outside a home there is a keypad that will open the garage if the correct four-digit code is entered. (a) How many codes are possible? (b) What is the probability of entering the correct code on the first try, assuming that the owner doesn’t remember the
> Companies whose stocks are listed on the NASDAQ stock exchange have their company name represented by either four or five letters (repetition of letters is allowed). What is the maximum number of companies that can be listed on the NASDAQ?
> Companies whose stocks are listed on the New York Stock Exchange (NYSE) have their company name represented by either one, two, or three letters (repetition of letters is allowed). What is the maximum number of companies that can be listed on the New Yor
> The music player on an iPhone plays each of 10 songs. Once a song is played, it is not repeated until all the songs have been played. In how many different ways can the player play the 10 songs?
> A salesperson must travel to eight cities to promote a new marketing campaign. How many different trips are possible if any route between cities is possible?
> In how many ways can 15 students be lined up?
> Suppose Dan is going to create a Spotify playlist with 12 songs. In how many ways can the 12 songs be played without repetition?
> A woman has five blouses and three skirts. Assuming that they all match, how many different outfits can she wear?
> A man has six shirts and four ties. Assuming that they all match, how many different shirt-and-tie combinations can he wear?
> A coach must select two players to serve as captains. He wants to randomly select two players to be the captains. Obtain a simple random sample of size 2 from the following list: Mady, Breanne, Evin, Tori, Emily, Clair, Caty, Jory, Payton, Jordyn. Write
> List all the combinations of four objects a, b, c, and d taken two at a time. What is 4C2?
> List all the combinations of five objects a, b, c, d, and e taken two at a time. What is 5C2?
> List all the permutations of four objects a, b, c, and d taken two at a time without repetition. What is 4P2?
> List all the permutations of five objects a, b, c, d, and e taken two at a time without repetition. What is 5P2?
> 30C4
> 48C3
> 40C40
> 52C1
> 12C3
> 10C2
> As part of a college literature course, students must read three classic works of literature from the provided list. Obtain a simple random sample of size 3 from this list. Write a short description of the process you used to generate your sample.
> 9C2
> 8C3
> 9P4
> 8P3
> 4P0
> 5P0
> 7P7
> 7P2
> 6P2
> In your own words, define explanatory variable and response variable.
> 1!
> 0!
> 12!
> 10!
> 7!
> 5!
> The factorial symbol, n!, is defined as n! =______ and 0! =_______ .
> True or False: In a combination problem, order is not important.
> A_____ is an arrangement of r objects chosen from n distinct objects without repetition and without regard to order.
> Suppose that E and F are two events and that N(E and F) = 380 and N(E) = 925. What is P(F | E)?
> Discuss the ethics behind scraping data from the Internet. In particular, answer the following questions. What is the responsibility of the website host to protect your information (data)? What are your responsibilities to protect your information? For a
> Suppose that E and F are two events and that N(E and F) = 420 and N(E) = 740. What is P(F | E)?
> Suppose that E and F are two events and that P(E and F) = 0.21 and P(E) = 0.4. What is P(F | E)?
> Suppose that E and F are two events and that P(E and F ) = 0.6 and P(E) = 0.8. What is P(F | E)?
> If P(E) = 0.6 and P(E | F) = 0.34, are events E and F independent?
> The notation P(F | E) means the probability of event ____ given event_____ .
> Is there a “path” to success? Brookings scholars Ron Haskins and Isabel Sawhill suggest the path to success is: education, followed by work, followed by marriage, followed by children. Sociologists Wendy Wang and W. Bradford Wilcox tracked a cohort of yo
> Refer to the contingency table in Problem 18 that relates social media use and age. Determine P(uses social media) and P(uses social media | 35–44 years). Are the events “uses social media” and “35–44 years” independent?
> Refer to the contingency table in Problem 17 that relates age and likelihood to buy American. Determine P(45 -54 years old) and P(45 -54 years old | more likely). Are the events “45 -54 years old” and “more likely” independent?
> Suppose that a poll is being conducted in the village of Lemont. The pollster identifies her target population as all residents of Lemont 18 years old or older. This population has 6494 people. (a) Compute the probability that the first resident selected
> Suppose that a computer chip company has just shipped 10,000 computer chips to a computer company. Unfortunately, 50 of the chips are defective. (a) Compute the probability that two randomly selected chips are defective using conditional probability. (b)
> Name three ways that web scraping can be used to obtain data.
> A flush in the card game of poker occurs if a player gets five cards that are all the same suit (clubs, diamonds, hearts, or spades). Answer the following questions to obtain the probability of being dealt a flush in five cards. (a) We initially concentr
> Mammograms are used to detect breast cancer. Suppose a mammogram is known to be 80% accurate, which means P(positive mammogram | cancer) = 0.80. Suppose in the United States, 40 million women are tested for breast cancer with mammograms and, of these, 20
> The following data represent political party by age from a random sample of registered Iowa Voters. (a) Are the events “Republican” and “30–44” independent? Justify your answer. (b) Are the events “Democrat” and “65+” independent? Justify your answer. (c
> The following data represent the number of different communication activities (e.g., cell phone, text messaging, e-mail, Instagram, and so on) used by a random sample of teenagers over the past 24 hours. (a) Are the events “male” and “0 activities” indep
> Using the procedure given in Problem 33, compute the probability that at least 2 people in a room of 23 people share the same birthday.
> Determine the probability that at least 2 people in a room of 10 people share the same birthday, ignoring leap years and assuming each birthday is equally likely, by answering the following questions: (a) Compute the probability that 10 people have 10 di
> According to the U.S. Bureau of Labor Statistics, there is a 4.9% probability that a randomly selected employed individual has more than one job (a multiple-job holder). Also, there is a 46.6% probability that a randomly selected employed individual is m
> According to the National Center for Health Statistics, there is a 20.3% probability that a randomly selected resident of the United States aged 18 years or older is a smoker. In addition, there is a 44.5% probability that a randomly selected resident of
> The local golf store sells an “onion bag” that contains 35 “experienced” golf balls. Suppose that the bag contains 20 Titleists, 8 Maxflis, and 7 Top Flites. Use a tree diagram like the one in Example 5 to answer the following: (a) What is the probabilit
> A bag of 30 tulip bulbs purchased from a nursery contains 12 red tulip bulbs, 10 yellow tulip bulbs, and 8 purple tulip bulbs. Use a tree diagram like the one in Example 5 to answer the following: (a) What is the probability that two randomly selected tu
> The following abstract appears in The New England Journal of Medicine: BACKGROUND. The relation between passive smoking and lung cancer is of great public health importance. Some previous studies have suggested that exposure to environmental tobacco smok
> Interviews of 100 adults 18 years of age or older, conducted nationwide, found that 44% could state the minimum age required for the office of U.S. president. Source: Newsweek Magazine.
> Because of a manufacturing error, three cans of regular soda were accidentally filled with diet soda and placed into a 12-pack. Suppose that two cans are randomly selected from the 12-pack. (a) Determine the probability that both contain diet soda. (b) D
> Suppose that a Spotify playlist has 13 tracks. After listening to all the songs, you decide that you like 5 of them. With the random feature on the playlist, each of the 13 songs is played once in random order. Find the probability that among the first t
> My wife has organized a monthly neighborhood party. Five people are involved in the group: Yolanda (my wife), Lorrie, Laura, Kim, and Anne Marie. They decide to randomly select the first and second home that will host the party. What is the probability t
> This past semester, I had a small business calculus section. The students in the class were Mike, Neta, Jinita, Kristin, and Dave. Suppose that I randomly select two people to go to the board to work problems. What is the probability that Dave is the fir
> Suppose that two cards are randomly selected from a standard 52-card deck. (a) What is the probability that the first card is a club and the second card is a club if the sampling is done without replacement? (b) What is the probability that the first car
> Suppose that two cards are randomly selected from a standard 52-card deck. (a) What is the probability that the first card is a king and the second card is a king if the sampling is done without replacement? (b) What is the probability that the first car
> A committee consisting of four women and three men will randomly select two people to attend a conference in Hawaii. Find the probability that both are women.
> Suppose that you just received a shipment of six televisions and two are defective. If two televisions are randomly selected, compute the probability that both televisions work. What is the probability that at least one does not work?
> Use the results of Problem 44 in Section 5.2 to answer the following. (a) Among those who text while driving, what is the probability that a randomly selected individual was issued no tickets last year? (b) Among those who were issued no tickets last yea
> The following data represent the number of drivers involved in a fatal crash in 2016 in various light and weather conditions. (a) Among fatal crashes in normal weather, what is the probability that a randomly selected fatal crash occurs at dawn/dusk? (b)
> In an infamous study, researchers suggested that left-handed individuals died younger than right-handed individuals. In the study, researchers identified 987 individuals who died in 1990 and then used historical records to determine birth year as well as
> Adult Americans (18 years or older) were asked whether they used social media (Facebook, Twitter, and so on) regularly. The following table is based on the results of the survey. (a) What is the probability that a randomly selected adult American uses so
> In a recent Harris Poll, a random sample of adult Americans (18 years and older) was asked, “When you see an ad emphasizing that a product is ‘Made in America,’ are you more likely to buy it, less likely to buy it, or neither more nor less likely to buy
> According to the U.S. Census Bureau, 17.9% of U.S. households are in the Northeast. In addition, 5.4% of U.S. households earn $100,000 per year or more and are located in the Northeast. Determine the probability that a randomly selected U.S. household ea
