Question: Define each of the following. (a) Probability

> 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

> 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.

> 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.

> You suspect a 6-sided die to be loaded and conduct a probability experiment by rolling the die 400 times. The outcome of the experiment is listed in the table below. Do you think the die is loaded? Why?

> Determine whether the probabilities below are computed using classical methods, empirical methods, or subjective methods. (a) The probability of having eight girls in an eight-child family is 0.00390625. (b) On the basis of a survey of 1000 families with

> In 2011, Six Flags St. Louis had 10 roller coasters: The Screamin’ Eagle, The Boss, River King Mine Train, Batman the Ride, Mr. Freeze, Ninja, Tony Hawk’s Big Spin, Evel Knievel, Xcalibur, and Sky Screamer. Of these, The Boss, The Screamin’ Eagle, and Ev

> John, Roberto, Clarice, Dominique, and Marco work for a publishing company. The company wants to send two employees to a statistics conference in Orlando. To be fair, the company decides that the two individuals who get to attend will have their names ra

> Which of the assignments of probabilities should be used if tails is twice as likely to occur as heads?

> Which of the assignments of probabilities should be used if the coin is known to always come up tails?

> A survey is conducted asking 400 people, “Do you prefer Coke or Pepsi?”

> Which of the assignments of probabilities should be used if the coin is known to be fair?

> Which of the assignments of probabilities are consistent with the definition of a probability model?

> On your drives to school each day you feel like there is a light that is always red when you reach it. You decide to record data to determine the likelihood of arriving at the light while it is red. Open the data set 5_1_38 at www.pearsonhighered.com/sul

> Your daily commute to work requires that you cross railroad tracks. At this particular railroad crossing the trains tend to be long and slow. So, getting stopped by a train will likely make you late for work. You start recording data to determine the lik

> A survey was conducted by Wakefield Research in which participants were asked to disclose their favorite night to order takeout for dinner. The following data are based on their results. (a) Construct a probability model for favorite night to order takeo

> The table shows the movement of Walt Disney stock for 30 randomly selected trading days. “Up” means the stock price increased in value for the day. “Down” means the stock price decreased in value for the day, and “No Change” means the stock price closed

> The following data represent the number of live multiple-delivery births (three or more babies) in 2017 for women 15 to 54 years old. (a) Construct a probability model for number of multiple births. (b) In the sample space of all multiple births, are mul

> A police officer randomly selected 642 police records of larceny thefts. The following data represent the number of offenses for various types of larceny thefts. (a) Construct a probability model for type of larceny theft. (b) Are purse snatching larceni

> In a national survey conducted by the Centers for Disease Control to determine college students’ health-risk behaviors, college students were asked, “How often do you wear a seatbelt when driving a car?” The frequencies appear in the following table: (a)

> In a national survey conducted by the Centers for Disease Control to determine college students’ health-risk behaviors, college students were asked, “How often do you wear a seatbelt when riding in a car driven by someone else?” The frequencies appear in

> A study in which balding men were compared with non-balding men at one point in time found that balding men were 70% more likely to have heart disease. Source: USA Today, April 4, 2013.

> In Problem 29, we learned that for some diseases, such as sickle-cell anemia, an individual will get the disease only if he or she receives both recessive alleles. This is not always the case. For example, Huntington’s disease only requires one dominant

> A gene is composed of two alleles, either dominant or recessive. Suppose that a husband and wife, who are both carriers of the sickle-cell anemia allele but do not have the disease, decide to have a child. Because both parents are carriers of the disease

> Exclude leap years from the following calculations and assume each birthday is equally likely: (a) Determine the probability that a randomly selected person has a birthday on the 1st day of a month. Interpret this probability. (b) Determine the probabili

> In the game of roulette, a wheel consists of 38 slots numbered 0, 00, 1, 2, ……., 36. (See the photo.) To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots. (a) Determine the sample space. (b) Deter

> The Chicago Tribune analyzed 17,713 complaints by citizens against Chicago police officers. Source: Chicago Tribune, June 14, 2015. (a) Of the 17,713 complaints against police officers, it was found that 7296 were accompanied by a signed affidavit, which

> The Wall Street Journal regularly publishes an article entitled “The Count.” In one article, The Count looked at 1000 randomly selected home runs in Major League Baseball. Source: Wall Street Journal, September 24, 2014. (a) Of the 1000 home runs, it was

> In a survey of 1100 female adults (18 years of age or older), it was determined that 341 volunteered at least once in the past year. (a) What is the probability that a randomly selected adult female volunteered at least once in the past year? (b) Interpr

> A survey of 500 randomly selected high school students determined that 288 played organized sports. (a) What is the probability that a randomly selected high school student plays organized sports? (b) Interpret this probability.

> Compute the probability of the event F = “an odd number.”

> Compute the probability of the event E = “an even number less than 9.”

> Seventh-grade students are randomly divided into two groups. One group is taught math using traditional techniques; the other is taught math using a reform method. After 1 year, each group is given an achievement test to compare proficiency.

> Compute the probability of the event F = {3, 5, 9, 10}

> Compute the probability of the event E = {1, 2, 3}.

> According to the American Veterinary Medical Association, the proportion of households owning a dog is 0.372. What is the probability that a randomly selected household owns a dog?

> According to the U.S. Department of Education, 42.8% of 3-year-olds are enrolled in day care. What is the probability that a randomly selected 3-year-old is enrolled in day care?