Question: Merck & Co. conducted a study to test
Merck & Co. conducted a study to test the promise of its experimental AIDS vaccine (The Boston Globe, September 22, 2007). Volunteers in the study were all free of the human immunodeficiency virus (HIV), which causes AIDS, at the start of the study, but all were at high risk for getting the virus. Volunteers were given either the vaccine or a dummy shot; 24 of 741 volunteers who got the vaccine became infected with HIV, whereas 21 of 762 volunteers who got the dummy shot became infected with HIV. The following table summarizes the results of the study. 
a. Convert the contingency table into a joint probability table. b. What is the probability that a randomly selected volunteer got vaccinated? c. What is the probability that a randomly selected volunteer became infected with the HIV virus? d. If the randomly selected volunteer was vaccinated, what is the probability that he/she got infected? e. Are the events “Vaccinated†and “Infected†independent? Explain using probabilities. Given your answer, is it surprising that Merck & Co. ended enrollment and vaccination of volunteers in the study? Explain.
Transcribed Image Text:
Vaccinated Dummy Shot Infected 24 21 Not Infected 717 741
> Consider the following scenarios to determine if the mentioned combination of attributes represents a union or an intersection. a. There are two courses that seem interesting to you, and you would be happy if you can take at least one of them. b. There a
> Apparently, depression significantly increases the risk of developing dementia later in life (BBC News, July 6, 2010). In a study, it was reported that 22% of those who had depression went on to develop dementia, compared to only 17% of those who did not
> An analyst predicts that there is a 40% chance that the U.S. economy will perform well. If the U.S. economy performs well, then there is an 80% chance that Asian countries will also perform well. On the other hand, if the U.S. economy performs poorly, th
> It has been reported that women end up unhappier than men later in life, even though they start out happier (Yahoo News, August 1, 2008). Early in life, women are more likely to fulfill their family life and financial aspirations, leading to greater over
> A study in the Journal of the American Medical Association (February 20, 2008) found that patients who go into cardiac arrest while in the hospital are more likely to die if it happens after 11 pm. The study investigated 58,593 cardiac arrests that occur
> At a local bar in a small Midwestern town, beer and wine are the only two alcoholic options. The manager noted that of all male customers who visited over the weekend, 150 ordered beer, 40 ordered wine, and 20 asked for soft drinks. Of female customers,
> It has generally been believed that it is not feasible for men and women to be just friends (The New York Times, April 12, 2012). Others argue that this belief may not be true anymore since gone are the days when men worked and women stayed at home and t
> A professor of management has heard that eight students in his class of 40 have landed an internship for the summer. Suppose he runs into two of his students in the corridor. a. Find the probability that neither of these students has landed an internship
> According to the CGMA Economic Index, which measures executive sentiment across the world, 18% of all respondents expressed optimism about the global economy (www.aicpa.org, March 29, 2012). Moreover, 22% of the respondents from the United States and 9%
> A study shows that unemployment does not impact males and females in the same way (Newsweek, April 20, 2009). According to a Bureau of Labor Statistics report, 8.5% of those who are eligible to work are unemployed. The unemployment rate is 8.8% for eligi
> Let P(A) = 0.65, P(B) = 0.30, and P (A ∣ B) = 0.45. a. Calculate P (A ∩ B). b. Calculate P (A ∪ B). c. Calculate P (B ∣ A).
> Wooden boxes are commonly used for the packaging and transportation of mangoes. A convenience store in Morganville, New Jersey, regularly buys mangoes from a wholesale dealer. For every shipment, the manager randomly inspects two mangoes from a box conta
> Consider the following scenarios to determine if the mentioned combination of attributes represents a union or an intersection. a. A marketing firm is looking for a candidate with a business degree and at least five years of work experience. b. A family
> Anthony Papantonis, owner of Nauset Construction, is bidding on two projects, A and B. The probability that he wins project A is 0.40 and the probability that he wins project B is 0.25. Winning Project A and winning Project B are independent events. a. W
> How much you smile in your younger days can predict your later success in marriage (www.msnbc.com, April 16, 2009). The analysis is based on the success rate in marriage of people over age 65 and their smiles when they were only 10 years old. Researchers
> The following frequency distribution shows the ages of India’s 40 richest individuals. One of these individuals is selected at random. a. What is the probability that the individual is between 50 and 60 years of age? b. What is the pr
> The Easy Credit Company reports the following table representing a breakdown of customers according to the amount they owe and whether a cash advance has been made. An auditor randomly selects one of the accounts. a. What is the probability that a cust
> Henry Chow is a stockbroker working for Merrill Lynch. He knows from past experience that there is a 70% chance that his new client will want to include U.S. equity in her portfolio and a 50% chance that she will want to include foreign equity. There is
> According to eMarketer estimates, 88.3% of 12- to 17-year-olds had a mobile phone in 2016. Among those with mobile phones, 84.0% had smartphones. Calculate the proportion of 12- to 17-year-olds who had smartphones.
> AccuScore calculated an 84% chance that there would be a fight during the game between the Anaheim Ducks and the Chicago Blackhawks, two of the National Hockey League’s most pugnacious teams (The Wall Street Journal, March 3, 2009). What are the odds for
> According to a global survey of 4,400 parents of children between the ages of 14 to 17, 44% of parents spy on their teen’s Facebook account (www.msnbc.com, April 25, 2012). Assume that American parents account for 10% of all parents of teens with Faceboo
> Prior to the Academy Awards ceremony in 2009, the United Kingdom bookmaker Ladbrokes reported the following odds for winning an Oscar in the category of best actress (The Wall Street Journal, February 20, 2009). a. Express the odds for each actress win
> David Barnes and his fiancée Valerie Shah are visiting Hawaii. At the Hawaiian Cultural Center in Honolulu, they are told that 2 out of a group of 8 people will be randomly picked for a free lesson of a Tahitian dance. a. What is the probability that bot
> Jacqueline Fibbe manages 10 employees at a small ice cream store in Beverly Farms, MA. She assigns three employees for each eight-hour shift. a. If order is not important, in how many different ways can she select three employees from the total of 10 for
> Jane Peterson has taken Amtrak to travel from New York to Washington, DC, on six occasions, of which three times the train was late. Therefore, Jane tells her friends that the probability that this train will arrive on time is 0.50. Would you label this
> A horse-racing fan is contemplating the many different outcomes in an eight-horse race. a. How many different outcomes are possible if only the first three places are considered and ranking (first, second, and third) is important? b. If each of the outco
> There are 10 players on the local basketball team. The coach decides to randomly pick 5 players to start the game. a. In how many different ways can the coach select 5 players to start the game if order does not matter? b. In how many different ways can
> Twenty cancer patients volunteer for a clinical trial. Ten of the patients will receive a placebo and 10 will receive the trial drug. In how many different ways can the researchers select 10 patients to receive the trial drug from the total of 20?
> At a local elementary school, a principal is making random class assignments for her 8 teachers. Each teacher must be assigned to exactly one job. In how many ways can the assignments be made?
> Calculate the following values. a. 7! and 3! b. 7C3 c. 7P3
> Calculate the following values. a. 8! and 6! b. 8C6 c. 8P6
> An analyst thinks that next year there is a 20% chance that the world economy will be good, a 50% chance that it will be neutral, and a 30% chance that it will be poor. She also predicts probabilities that the performance of a start-up firm, Creative Ide
> On Sunday, July 11, 2010, Spain and the Netherlands played in the 2010 World Cup Final in Johannesburg. On the eve of the final, many betting lines were offering Spain’s odds for winning at 15:8 (Odds checker website). a. Spain won the World Cup. Suppos
> A crucial game of the Los Angeles Lakers basketball team depends on the health of their key player. According to his doctor’s report, there is a 40% chance that he will be fully fit to play, a 30% chance that he will be somewhat fit to play, and a 30% ch
> According to data from the National Health and Nutrition Examination Survey, 33% of white, 49.6% of black, 43% of Hispanic, and 8.9% of Asian women are obese. In a representative town, 48% of women are white, 19% are black, 26% are Hispanic, and the rema
> According to a study, cell phones are the main medium for teenagers to stay connected with friends and family (CNN, March 19, 2012). It is estimated that 90% of older teens and 60% of younger teens own a cell phone. Suppose 70% of all teens are older tee
> Survey data, based on 65,000 mobile phone subscribers, shows that 44% of the subscribers use smartphones (Forbes, December 15, 2011). Based on this information, you infer that the probability that a mobile phone subscriber uses a smartphone is 0.44. Woul
> The State Police are trying to crack down on speeding on a particular portion of the Massachusetts Turnpike. To aid in this pursuit, they have purchased a new radar gun that promises greater consistency and reliability. Specifically, the gun advertises ±
> An analyst expects that 20% of all publicly traded companies will experience a decline in earnings next year. The analyst has developed a ratio to help forecast this decline. If the company is headed for a decline, there is a 70% chance that this ratio w
> Christine has always been weak in mathematics. Based on her performance prior to the final exam in Calculus, there is a 40% chance that she will fail the course if she does not have a tutor. With a tutor, her probability of failing decreases to 10%. Ther
> Let a sample space be partitioned into three mutually exclusive and exhaustive events, B1, B2, and B3. Complete the following probability table. Prior Conditional Joint Posterior Probabilities Probabilities Probabilities Probabilities P(B,) = 0.10 P
> Complete the following probability table Prior Conditional Joint Posterior Probability Probability Probability Probability Р(B) 3D 0.85 Р(A | В) 3D 0.05 P(ANB) = P(B | A) = P(B c) = P(A I BC) = 0.80 P(AN BC) = Р(вс | А) - Total : P(A) = Total = %D %
> Complete the following probability table: Prior Conditional Joint Posterior Probability Probability Probability Probability P(A) = 0.30 P(B | A) = 0.25 P(A N B) = P(A | B) = %3D P(AC) = P(B A c) = 0.80 P(ACN B) = P(AC | B) = Total = P(B) = Total =
> At four community health centers on Cape Cod, Massachusetts, 15,164 patients were asked to respond to questions designed to detect depression (The Boston Globe, June 11, 2008). The survey produced the following results. a. What is the probability that
> Let P(A) = 0.70, P (B ∣ A) = 0.55, and P (B ∣ Ac) = 0.10. Use a probability tree to calculate the following probabilities: a. P(Ac) b. P (A ∩ B) and P (Ac ∩ B) c. P(B) d. P (A ∣ B)
> Let P(B) = 0.60, P (A ∣ B) = 0.80, and P (A ∣ Bc) = 0.10. Calculate the following probabilities: a. P(Bc) b. P (A ∩ B) and P (A ∩ Bc) c. P (A) d. P (B ∣ A)
> The research team at a leading perfume company is trying to test the market for its newly introduced perfume. In particular the team wishes to look for gender and international differences in the preference for this perfume. They sample 2,500 people inte
> More and more households are struggling to pay utility bills given high heating costs (The Wall Street Journal, February 14, 2008). Particularly hard hit are households with homes heated with propane or heating oil. Many of these households are spending
> A sample space, S, yields four simple events, A, B, C, and D, such that P(A) = 0.35, P(B) = 0.10, and P(C ) = 0.25. a. Find P(D). b. Find P(Cc). c. Find P (A ∪ B).
> According to a Michigan State University researcher, Americans are becoming increasingly polarized on issues pertaining to the environment (msutoday.msu.edu, April 19, 2011). It is reported that 70% of Democrats see signs of global warming as compared to
> A poll asked 16- to 21-year-olds whether or not they are likely to serve in the U.S. military. The following joint probability table, cross-classified by gender and race, reports them proportion of those polled who responded that they are likely or very
> A report suggests that business majors spend the least amount of time on course work than all other college students (The NewYork Times, November 17, 2011). A provost of a university decides to conduct a survey where students are asked if they study hard
> According to an online survey by Harris Interactive for job site CareerBuilder.com, more than half of IT (information technology) workers say they have fallen asleep at work (InformationWeek, September 27, 2007). Sixty-four percent of government workers
> Many communities are finding it more and more difficult to fill municipal positions such as town administrators, finance directors, and treasurers. The following table shows the proportion of municipal managers by age group in the United States for the y
> Consider the following joint probability table. a. What is the probability that A occurs? b. What is the probability that B2 occurs? c. What is the probability that Ac and B4 occur? d. What is the probability that A or B3 occurs? e. Given that B2 has o
> Consider the following contingency table. a. Convert the contingency table into a joint probability table. b. What is the probability that A occurs? c. What is the probability that A and B occur? d. Given that B has occurred, what is the probability th
> A study challenges the media narrative that foreclosures are dangerously widespread (The New York Times, March 2, 2009). According to this study, 62% of all foreclosures were centered in only four states, namely, Arizona, California, Florida, and Nevada.
> According to results from the Spine Patient Outcomes Research Trial, or SPORT, surgery for a painful, common back condition resulted in significantly reduced back pain and better physical function than treatment with drugs and physical therapy (The Wall
> According to a survey by two United Nations agencies and a nongovernmental organization, two in every three women in the Indian capital of New Delhi are likely to face some form of sexual harassment in a year (BBC World News, July 9, 2010). The study als
> You roll a die with the sample space S = {1, 2, 3, 4, 5, 6}. You define A as {1, 2, 3}, B as {1, 2, 3, 5, 6}, C as {4, 6}, and D as {4, 5, 6}. Determine which of the following events are exhaustive and/or mutually exclusive. a. A and B b. A and C c. A an
> A study shows that unemployment does not impact white-collar and blue-collar workers equally (Newsweek, April 20, 2009). According to the Bureau of Labor Statistics report, while the national unemployment rate is 8.5%, it is only 4.3% for those with a co
> According to the Census’s Population Survey, the percentage of children with two parents at home is the highest for Asians and lowest for blacks (USA TODAY, February 26, 2009). It is reported that 85% of Asian, 78% of white, 70% of Hispanic, and 38% of b
> Christine Wong has asked Dave and Mike to help her move into a new apartment on Sunday morning. She has asked them both, in case one of them does not show up. From past experience, Christine knows that there is a 40% chance that Dave will not show up and
> Despite the repeated effort by the government to reform how Wall Street pays its executives, some of the nation’s biggest banks are continuing to pay out bonuses nearly as large as those in the best years before the Great Recession (The Washington Post,
> An alarming number of U.S. adults are either overweight or obese. The distinction between overweight and obese is made on the basis of body mass index (BMI), expressed as weight/height2. An adult is considered overweight if the BMI is 25 or more but less
> Apple products have become a household name in America, with 51% of all households owning at least one Apple product (CNN, March 19, 2012). In the Midwest, the likelihood of owning an Apple product is 61% for households with kids and 48% for households w
> A manufacturing firm just received a shipment of 20 assembly parts, of slightly varied sizes, from a vendor. The manager knows that there are only 15 parts in the shipment that would be suitable. He examines these parts one at a time. a. Find the probabi
> In general, shopping online is supposed to be more convenient than going to stores. However, according to a Harris Interactive poll, 87% of people have experienced problems with an online transaction (The Wall Street Journal, October 2, 2007). Forty-two
> Mike Danes has been delayed in going to the annual sales event at one of his favorite apparel stores. His friend has just texted him that there are only 20 shirts left, of which 8 are in size M, 10 in size L, and 2 in size XL. Also 9 of the shirts are wh
> An analyst estimates that the probability of default on a seven-year AA-rated bond is 0.06, while that on a seven-year A-rated bond is 0.13. The probability that they will both default is 0.04. a. What is the probability that at least one of the bonds de
> Records show that 5% of all college students are foreign students who also smoke. It is also known that 50% of all foreign college students smoke. What percent of the students at this university are foreign?
> A sample space S yields five equally likely events, A, B, C, D, and E. a. Find P(D). b. Find P(Bc). c. Find P (A ∪ C ∪ E).
> Dr. Miriam Johnson has been teaching accounting for over 20 years. From her experience, she knows that 60% of her students do homework regularly. Moreover, 95% of the students who do their homework regularly pass the course. She also knows that 85% of he
> Despite government bailouts and stimulus money, unemployment in the United States had not decreased significantly as economists had expected (U.S. News & World Report, July 2, 2010). Many analysts predicted only an 18% chance of a reduction in U.S. unemp
> The probabilities that stock A will rise in price is 0.40 and that stock B will rise in price is 0.60. Further, if stock B rises in price, the probability that stock A will also rise in price is 0.50. a. What is the probability that at least one of the s
> You apply for a position at two firms. Let event A represent the outcome of getting an offer from the first firm and event B represent the outcome of getting an offer from the second firm. a. Explain why events A and B are not exhaustive. b. Explain why
> Only 20% of students in a college ever go to their professor during office hours. Of those who go, 30% seek minor clarification and 70% seek major clarification. a. What is the probability that a student goes to the professor during her office hours for
> Survey data, based on 65,000 mobile phone subscribers, show that 44% of the subscribers use smartphones (Forbes, December 15, 2011). Moreover, 51% of smartphone users are women. a. Find the probability that a mobile phone subscriber is a woman who uses a
> Consider the following probabilities: P(A) = 0.40, P(B) = 0.50, and P (Ac ∩ Bc) = 0.24. Find: a. P (Ac ∣ Bc) b. P (Ac ∪ Bc) c. P (A ∪ B)
> Consider the following probabilities: P(Ac) = 0.30, P(B) = 0.60, and P (A ∩ Bc) = 0.24. Find: a. P (A ∣ Bc) b. P (Bc ∣ A) c. Are A and B independent events? Explain.
> Consider the following probabilities: P(A) = 0.25, P(Bc) = 0.40, and P (A ∩ B) = 0.08. Find: a. P(B) b. P (A ∣ B) c. P (B ∣ A)
> Let P(A) = 0.15, P(B) = 0.10, and P (A ∩ B) = 0.05. a. Are A and B independent events? Explain. b. Are A and B mutually exclusive events? Explain. c. What is the probability that neither A nor B takes place?
> Let P(A) = 0.65, P(B) = 0.30, and P (A ∣ B) = 0.45. a. Are A and B independent events? Explain. b. Are A and B mutually exclusive events? Explain. c. What is the probability that neither A nor B takes place?
> Express each of the probabilities in the preceding question as a. odds assessed by Sunil for obtaining tails. b. odds assessed by John for receiving straight A’s. c. odds assessed by the reporter for a Republican coming out of the room.
> Let A and B be independent events with P(A) = 0.40 and P(B) = 0.50. a. Calculate P (A ∩ B). b. Calculate P ((A ∪ B)c). c. Calculate P (A ∣ B).
> Let A and B be mutually exclusive events with P(A) = 0.25 and P(B) = 0.30. a. Calculate P (A ∩ B). b. Calculate P (A ∪ B). c. Calculate P (A ∣ B).
> Determine whether the following probabilities are best categorized as subjective, empirical, or classical probabilities. a. Before flipping a fair coin, Sunil assesses that he has a 50% chance of obtaining tails. b. At the beginning of the semester, Joh
> Define the following terms associated with preferred stock: a. Cumulative feature b. Participation c. Call feature
> What is the relationship between par value, market value, and book value for the following? a. Long-term debt b. Preferred stock
> Suppose a company simultaneously sold two long-term debt issues at par: 9⅛ percent senior debentures and 9⅜ percent subordinated debentures. What risk-return trade-off would be faced by an investor who was considering one of these issues?
> Describe the basic features of each of the following types of bonds: a. Mortgage bonds b. Debentures c. Subordinated debentures d. Equipment trust certificates e. Collateral trust bonds f. Income bonds
> Define the following terms associated with long-term debt: a. Indenture b. Trustee c. Call feature d. Sinking fund e. Conversion feature f. Coupon rate
> Konawalski’s Kustom Erdapfel Chips, Inc., is the maker of gourmet German-style potato chips. The company began business three years ago in rural North Carolina and grew quickly as the product became known. Konawalski is now poised for national growth. So
> Blue Moon Corporation has one million shares of common stock outstanding. In a typical annual election for the board of directors, shareholders representing 70 percent of the shares outstanding exercise their right to vote. The company has nine members o
> The following stock quotations were recently reported in The Wall Street Journal: a. What are the dividend yields on the common stock of AT&T, Boeing, and Johnson & Johnson? b. What possible explanation can you give for the differences in the
> The Alpha Tool Corporation has never paid a dividend, but the new company president has announced that the firm would pay its first dividend exactly two years from now. That dividend is expected to be $2 per share. It is anticipated that this dividend wi
> Whitehurst Associates is considering a substantial investment in the stock of Ivanhoe Enterprises. Ivanhoe currently (time 0) pays a dividend of $3 per share. This dividend is expected to grow at 15 percent per year for the next three years and 10 percen
> What effect do increasing inflation expectations have on the required returns of investors in common stock?
> Watkins, Inc., has experienced an explosion in demand for its ram football novelties. The firm currently (time 0) pays a dividend of $0.50 per share. This dividend is expected to increase to $1.00 per share one year from now. It is expected to grow at a
> The Blinkelman Corporation has just announced that it plans to introduce a new solar panel that will greatly reduce the cost of solar energy. As a result, analysts now expect the company’s earnings, currently (year 0) $1 per share to grow by 50 percent p
