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 positive when the antibody is not present (a false positive) is 0.005. Suppose that the ELISA is given to five randomly selected people who do not have the HIV antibody. (a) What is the probability that the ELISA comes back negative for all five people? (b) What is the probability that the ELISA comes back positive for at least one of the five people?
> 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
> 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
> 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.
> Suppose that events E and F are independent, P(E) = 0.7 and P(F) = 0.9. What is the P(E and F)?
> Researchers Sally Tracy and associates undertook a cross-sectional study looking at the method of delivery and cost of delivery for first-time “low risk” mothers under three delivery scenarios: (1) Caseload midwifery (2) Standard hospital care (3) Privat
> Suppose that events E and F are independent, P(E) = 0.3 and P(F) = 0.6. What is the P(E and F)?
> Determine whether the events E and F are independent or dependent. Justify your answer. (a) E: The battery in your cell phone is dead. F: The batteries in your calculator are dead. (b) E: Your favorite color is blue. F: Your friend’s favorite
> Determine whether the events E and F are independent or dependent. Justify your answer. (a) E: Speeding on the interstate. F: Being pulled over by a police officer. (b) E: You gain weight. F: You eat fast food for dinner every night. (c) E:
> Suppose events E and F are disjoint. What is P(E and F)?
> If two events E and F are independent, P1E and F2 =______ .
> True or False: When two events are disjoint, they are also independent.
> The word or in probability implies that we use the _____ Rule.
> What does it mean when two events are disjoint?
> The following data represent the homework scores for the material on Polynomial and Rational Functions in Sullivan’s College Algebra course. (a) Construct a relative frequency distribution with a lower class limit of the first class equal to 30 and a cla
> In a study of the feasibility of a red-light camera program in the city of Milwaukee, the data below summarize the projected number of crashes at 13 selected intersections over a five-year period. (a) Identify the variables presented in the table. (b) St
> Are young couples who marry or cohabitate more likely to gain weight than those who stay single? Researchers followed 8000 men and women for 7 years. At the start of the study, none of the participants were married or living with a romantic partner. The
> Go to www.pearsonhighered.com/sullivanstats to obtain the data file SullivanStatsSurveyI using the file format of your choice for the version of the text you are using. The data represent the results of a survey conducted by the author. The variable “Tex
> The following data represent the number of drivers involved in a fatal crash in 2016 in various light and weather conditions. (a) Determine the probability that a randomly selected fatal crash in 2016 occurred in normal weather. (b) Determine the probabi
> Harris Interactive conducted a survey in which they asked adult Americans (18 years or older) whether they used social media (Facebook, Twitter, and so on) regularly. The following table is based on the results of the survey. /. (a) If an adult America
> A company is testing a new medicine for migraine headaches. In the study, 150 women were given the new medicine and 100 women were given a placebo. Each participant was directed to take the medicine when the first symptoms of a migraine occurred and then
> A guidance counselor at a middle school collected the following information regarding the employment status of married couples within his school’s boundaries. (a) What is the probability that, for a married couple selected at random, both spouses work? (
> The data in the following table show the results of a national study of 137,243 U.S. men that investigated the association between cigar smoking and death from cancer. Note: Current cigar smoker means cigar smoker at time of death. (a) If an individual i
> According to the U.S. Census Bureau, the probability that a randomly selected worker primarily drives a car to work is 0.764. The probability that a randomly selected worker primarily takes public transportation to work is 0.051. (a) What is the prob
> According to the U.S. Census Bureau, the probability that a randomly selected household speaks only English at home is 0.784. The probability that a randomly selected household speaks only Spanish at home is 0.123. (a) What is the probability that a rand
> A National Ambulatory Medical Care Survey administered by the Centers for Disease Control found that the probability a randomly selected patient visited the doctor for a blood pressure check is 0.593. The probability a randomly selected patient visited t
> According to the Centers for Disease Control, the probability that a randomly selected citizen of the United States has hearing problems is 0.151. The probability that a randomly selected citizen of the United States has vision problems is 0.093. Can we
> Is a television (TV) in the bedroom associated with obesity? Researchers questioned 379 twelve-year-old adolescents and concluded that the body mass index (BMI) of the adolescents who had a TV in their bedroom was significantly higher than the BMI of tho
> In the game of roulette, a wheel consists of 38 slots numbered 0, 00, 1, 2, c, 36. The odd-numbered slots are red, and the even-numbered slots are black. The numbers 0 and 00 are green. To play the game, a metal ball is spun around the wheel and is allow
> Exclude leap years from the following calculations: (a) Compute the probability that a randomly selected person does not have a birthday on November 8. (b) Compute the probability that a randomly selected person does not have a birthday on the 1st day of
> A standard deck of cards contains 52 cards, as shown in Figure 7. One card is randomly selected from the deck. (a) Compute the probability of randomly selecting a two or three from a deck of cards. (b) Compute the probability of randomly selecting a two
> A standard deck of cards contains 52 cards, as shown in Figure 7. One card is randomly selected from the deck. (a) Compute the probability of randomly selecting a heart or club from a deck of cards. (b) Compute the probability of randomly selecting a hea
> The following data represents the number of rooms in a random sample of U.S. housing units. (a) What is the probability that a randomly selected housing unit has four or more rooms? Interpret this probability. (b) What is the probability that a randomly
> In an effort to reduce the number of hospital-acquired conditions (such as infection resulting from the hospital stay), Medicare officials score hospitals on a 10-point scale with a lower score representing a better patient track record. The federal gove
> Draw a Venn diagram like that in Figure 8 that expands the General Addition Rule to three events. Use the diagram to write the General Addition Rule for three events.
> If events E and F are disjoint and the events F and G are disjoint, must the events E and G necessarily be disjoint? Give an example to illustrate your opinion.
> The following probability model shows the distribution of family structure among families with at least one child younger than 18 years of age. (a) Verify that this is a probability model. (b) What is the probability that a randomly selected family with
> The following probability model shows the distribution of injuries of youth baseball players, ages 5–14, according to researchers at SportsMedBC. (a) Verify that this is a probability model. (b) What is the probability that a randomly selected baseball i
> Is there an association between daily coffee consumption and the occurrence of skin cancer? Researchers asked 93,676 women to disclose their coffee- drinking habits and also determined which of the women had nonmelanoma skin cancer. The researchers concl
> Not a Top Flite.
> Not a Titleist.
> A Maxfli or Top Flite.
> A Titleist or Maxfli.
> If P(F) = 0.30, P(E or F) = 0.65, and P(E and F) = 0.15, find P(E).
> If P(E) = 0.60, P(E or F) = 0.85, and P(E and F) = 0.05, find P(F).
> P(Fc)
> P(Ec)
> P(E and F) if E and F are mutually exclusive
> P(E or F) if E and F are mutually exclusive
> Is there an association between level of happiness and the risk of heart disease? Researchers studied 1739 people over a 10-year period and asked questions about their daily lives and the hassles they face. The researchers also determined which individua
> P(E and F) if P(E or F) = 0.6
