Question: The following probability model shows the

> 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.

> 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 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

> P(E or F) if P(E and F) = 0.15

> List the outcomes in Fc. Find P(Fc).

> List the outcomes in Ec. Find P(Ec).

> List the outcomes in F and H. Are F and H mutually exclusive?

> List the outcomes in E and G. Are E and G mutually exclusive?

> List the outcomes in E or H. Now find P(E or H) by counting the number of outcomes in E or H. Determine P(E or H) using the General Addition Rule.

> List the outcomes in F or G. Now find P(F or G) by counting the number of outcomes in F or G. Determine P(F or G) using the General Addition Rule.

> List the outcomes in F and G. Are F and G mutually exclusive?

> List the outcomes in E and F. Are E and F mutually exclusive?

> Conservation agents netted 250 large-mouth bass in a lake and determined how many were carrying parasites.

> A study of 6076 adults in public rest rooms (in Atlanta, Chicago, New York City, and San Francisco) found that 23% did not wash their hands before exiting. Source: American Society for Microbiology and the Soap and Detergent Association.

> What does it mean when two events are complements?

> If E and F are not disjoint events, then P(E or F) =______ .

> If E and F are disjoint events, then P(E or F) =______ .

> Why is the following not a probability model?

> Verify that the following is a probability model. If the model represents the colors of M&Ms in a bag of milk chocolate M&Ms, explain what the model implies.

> Verify that the following is a probability model. What do we call the outcome “blue”?

> True or False: In a probability model, the sum of the probabilities of all outcomes must equal 1.

> Define each of the following. (a) Probability (b) Experiment (c) Event (d) Sample space (e) Equally likely outcomes (f) Impossible event (g) Unusual event

> Suppose that a probability is approximated to be zero based on empirical results. Does this mean the event is impossible? Explain.

> Suppose you live in a town with two hospitals—one large and the other small. On a given day in one of the hospitals, 60% of the babies who were born were girls. Which one do you think it is? Or, is it impossible to tell. Support your decision?

> Sixty patients with carpal tunnel syndrome are randomly divided into two groups. One group is treated weekly with both acupuncture and an exercise regimen. The other is treated weekly with the exact same exercise regimen, but no acupuncture. After 1 year

> In a September 19, 2010, article in Parade Magazine written to Ask Marilyn, Marilyn vos Savant was asked the following: Four identical sealed envelopes are on a table, one of which contains $100. You are to select one of the envelopes. Then the game host

> Describe the difference between classical and empirical probability.

> You are planning a trip to a water park tomorrow and the weather forecaster says there is a 70% chance of rain. Explain what this result means.

> Describe what an unusual event is. Should the same cutoff always be used to identify unusual events? Why or why not?

> In computing classical probabilities, all outcomes must be equally likely. Explain what this means.

> Explain the Law of Large Numbers. How does this law apply to gambling casinos?

> A friend of yours regularly plays the lottery but has never won. She says that she feels really good about this weekend’s drawing because she is due for a winning ticket. Explain the flaw in your friend’s reasoning.

> The following is a quote by Pierre-Simon Laplace: “To discover the best treatment to use in curing a disease, it is sufficient to test each treatment on the same number of patients, while keeping all circumstances perfectly similar. The superiority of th

> In placebo- controlled clinical trials for the drug Viagra, 734 subjects received Viagra and 725 subjects received a placebo (subjects did not know which treatment they received). The table below summarizes reports of various side effects that were repor

> Let’s say a player typically gets a hit in 3 out of every 10 at-bats (for a 0.300 batting average). Suppose the player has not had a hit in his previous four at-bats. In baseball, you will often hear an announcer say, “This player is due for a hit.” What

> Two hundred people are asked to perform a taste test in which they drink from two randomly placed, unmarked cups and are asked which drink they prefer.

> Each year the National Football League (NFL) runs a combine in which players who wish to be considered for the NFL draft must participate in a variety of activities. Go to www.pearsonhighered.com/sullivanstats to obtain the data file 5_1_50 using the fil

> The data set “Tornadoes_2017” located at www.pearsonhighered.com/sullivanstats contains a variety of variables that were measured for all tornadoes in the United States in 2017. (a) Construct a probability model for month in which the tornado occurred. (

> (a) In 2017, the median income of families in the United States was $60,336. What is the probability that a randomly selected family has an income greater than $60,336? (b) The middle 50% of enrolled freshmen at Washington University in St. Louis had SAT

> Conduct a survey in your school by randomly asking 50 students whether they drive to school. Based on the results of the survey, approximate the probability that a randomly selected student drives to school.