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 two songs played (a) You like both of them. Would this be unusual? (b) You like neither of them. (c) You like exactly one of them. (d) Redo (a)–(c) if a song can be replayed before all 13 songs are played (if, for example, track 2 can play twice in a row).
> 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
> 4P4
> 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
> 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
> According to the U.S. Census Bureau, 8.0% of 16- to 24-year-olds are high school dropouts. In addition, 2.1% of 16- to 24-year-olds are high school dropouts and unemployed. What is the probability that a randomly selected 16- to 24-year-old is unemployed
> According to the U.S. National Center for Health Statistics, 0.15% of deaths in the United States are 25- to 34-year-olds whose cause of death is cancer. In addition, 1.71% of all those who die are 25–34 years old. What is the probability that a randomly
> According to Pew Research, in 27% of marriages the woman has a bachelor’s degree and the marriage lasts at least 20 years. According to the Census Bureau, 35% of women have a bachelor’s degree. What is the probability a randomly selected marriage will la
> Suppose that a single card is selected from a standard 52-card deck. What is the probability that the card drawn is a king? Now suppose that a single card is drawn from a standard 52-card deck, but we are told that the card is a heart. What is the probab
> Suppose that a single card is selected from a standard 52-card deck. What is the probability that the card drawn is a club? Now suppose that a single card is drawn from a standard 52-card deck, but we are told that the card is black. What is the probabil
> The probability that a randomly selected individual in the United States 25 years and older has at least a bachelor’s degree is 0.094. The probability that an individual in the United States 25 years and older has at least a bachelor’s degree, given that
> According to the U.S. Census Bureau, the probability that a randomly selected head of household in the United States earns more than $100,000 per year is 0.202. The probability that a randomly selected head of household in the United States earns more th
> Researchers wanted to determine whether there is an association between mobile phone use and body mass index. To do so, 105,028 men and women aged 18 years or over from the United Kingdom were recruited and their cell-phone use behavior was studied (numb
> Suppose that E and F are two events and that P(E) = 0.4 and P(F | E) = 0.6. What is P(E and F)?
> Suppose that E and F are two events and that P(E) = 0.8 and P(F | E) = 0.4. What is P(E and F)?
> The word and in probability implies that we use the _____ Rule.
> Two events E and F are_____ if the occurrence of event E in a probability experiment does not affect the probability of event F.
> Ronald Fisher is considered the father of experimental design. Being of English descent, he was having afternoon tea with a colleague. The colleague’s wife entered the room as Fisher was pouring tea. Fisher offered tea to the lady. She politely accepted
> Ken and Dorothy like to fly to Colorado for ski vacations. Sometimes, however, they are late for their flight. On the air carrier they prefer to fly, the probability that luggage gets lost is 0.012 for luggage checked at least one hour prior to departure
> Suppose a mother already has three girls from three separate pregnancies. Does the fact that the mother already has three girls affect the likelihood of having a fourth girl? Explain.
> Fingerprints are now widely accepted as a form of identification. In fact, many computers today use fingerprint identification to link the owner to the computer. In 1892, Sir Francis Galton explored the use of fingerprints to uniquely identify an individ
> According to a Gallup Poll, about 17% of adult Americans bet on professional sports. Census data indicate that 48.4% of the adult population in the United States is male. (a) Assuming that betting is independent of gender, compute the probability that
> Suppose your financial advisor recommends three stocks to you. He claims the likelihood that the first stock will increase in value at least 10% within the next year is 0.7, the likelihood the second stock will increase in value at least 10% within the n
> Write a summary of the following opinion. The opinion was posted at abcnews.com. Include the type of study conducted, possible lurking variables, and conclusions. What is the message of the author of the article? Power Lines and Cancer—To Move or Not to
> According to the National Vital Statistics Report, 20.1% of all pregnancies result in weight gain in excess of 40 pounds (for singleton births). In addition, 49.5% of all pregnancies result in the birth of a baby girl. Assuming gender and weight gain are
> According to Internal Revenue Service records, 6.42% of all household tax returns are audited. According to the Humane Society, 39% of all households own a dog. Assuming dog ownership and audits are independent events, what is the probability a randomly
> Suppose that a satellite defense system is established in which four satellites acting independently have a 0.9 probability of detecting an incoming ballistic missile. What is the probability that at least one of the four satellites detects an incoming b
> Among 21- to 25-year-olds, 29% say they have driven while under the influence of alcohol. Suppose that three 21- to 25-year-olds are selected at random. Source: U.S. Department of Health and Human Services, reported in USA Today. (a) What is the probabil
> Suppose that Ralph gets a strike when bowling 30% of the time. (a) What is the probability that Ralph gets two strikes in a row? (b) What is the probability that Ralph gets a turkey (three strikes in a row)? (c) When events are independent, their complem
> Players in sports are said to have “hot streaks” and “cold streaks.” For example, a batter in baseball might be considered to be in a slump, or cold streak, if he has made 10 outs in 10 consecutive at-bats. Suppose that a hitter successfully reaches base
> See Problem 21. Suppose a particular airline component has a probability of failure of 0.03 and is part of a triple modular redundancy system. (a) What is the probability the system does not fail? (b) Engineers decide the probability of failure is too hi
> For a parallel structure of identical components, the system can succeed if at least one of the components succeeds. Assume that components fail independently of each other and that each component has a 0.15 probability of failure. (a) Would it be unusua
> In airline applications, failure of a component can result in catastrophe. As a result, many airline components utilize something called triple modular redundancy. This means that a critical component has two backup components that may be utilized sh
> Suppose that a company selects two people who work independently inspecting two-by-four timbers. Their job is to identify low-quality timbers. Suppose that the probability that an inspector does not identify a low-quality timber is 0.20. (a) What is the
> Magnum, LLC, is a web page design firm that has two designs for an online hardware store. To determine which is the more effective design, Magnum uses one page in the Denver area and a second page in the Miami area. For each visit, Magnum records the amo
> In finance, a derivative is a financial asset whose value is determined (derived) from a bundle of various assets, such as mortgages. Suppose a randomly selected mortgage has a probability of 0.01 of default. (a) What is the probability a randomly select
> In 1970, 92% of American 30-year-olds earned more than their parents did at age 30 (adjusted for inflation). In 2014, only 51% of American 30-year-olds earned more than their parents did at age 30. Source: Wall Street Journal, December 8, 2016. (a) What
> The probability that a randomly selected 40-year-old male will live to be 41 years old is 0.99757, according to the National Vital Statistics Report, Vol. 56, No. 9. (a) What is the probability that two randomly selected 40-year-old males will live to be
> Christmas lights are often designed with a series circuit. This means that when one light burns out the entire string of lights goes black. Suppose that the lights are designed so that the probability a bulb will last 2 years is 0.995. The success or fai
> The ELISA is a test to determine whether the HIV antibody is present. The test is 99.5% effective, which means that the test will come back negative if the HIV antibody is not present 99.5% of the time. The probability of a test coming back positiv
> Shawn lives near the border of Illinois and Missouri. One weekend he decides to play $1 in both state lotteries in hopes of hitting two jackpots. The probability of winning the Missouri Lotto is about 0.00000028357 and the probability of winning the Illi
> About 13% of the population is left-handed. If two people are randomly selected, what is the probability that both are left-handed? What is the probability that at least one is right-handed?
> What is the probability of obtaining 4 ones in a row when rolling a fair, six-sided die? Interpret this probability.
> What is the probability of obtaining five heads in a row when flipping a fair coin? Interpret this probability.
