An experiment has three steps with three outcomes possible for the first step, two outcomes possible for the second step, and four outcomes possible for the third step. How many experimental outcomes exist for the entire experiment? |
How many permutations of three items can be selected from a group of six? Use the letters A,B ,C , D,E , and F to identify the items, and list each of the permutations of items B, D, and F. |
A decision maker subjectively assigned the following probabilities to the four outcomes of an experiment: , , , and . Are these probability assignments valid? Explain.  |
The National Highway Traffic Safety Administration (NHTSA) collects traffic safety-related data for the U.S. Department of Transportation. According to NHTSA's data, 1042 fatal collisions in 2016 were the result of collisions with fixed objects (NHTSA website, https://www.careforcrashvictims.com/wp-content/uploads/2018/07/Traffic-Safety-Facts-2016_-Motor-Vehicle-Crash-Data-from-the-Fatality-Analysis-Reporting-System-FARS-and-the-General-Estimates-System-GES.pdf). The following table provides more information on these collisions.
Assume that a collision will be randomly chosen from this population. Round your answers to four decimal places. a. What is the probability of a fatal collision with a pole or post? b. What is the probability of a fatal collision with a guardrail? c. What type of fixed object is least likely to be involved in a fatal collision? What is the probability associated with this type of fatal collision? d. What type of object is most likely to be involved in a fatal collision? What is the probability associated with this type of fatal collision? | ||||||||||||||||||||||||
A 2018 Pew Research Center survey (Pew Research website) examined the use of social media platforms in the United States. The survey found that there is a 0.68probability that a randomly selected American will use Facebook and a 0.25probability that a randomly selected American will use LinkedIn. In addition, there is a 0.22probability that a randomly selected American will use both Facebook and LinkedIn. a. What is the probability that a randomly selected person will use Facebook or LinkedIn (to decimals)? b. What is the probability that a randomly selected person will not use either social media platform (to decimals)? |
High school seniors with strong academic records apply to the nation's most selective colleges in greater numbers each year. Because the number of slots remains relatively stable, some colleges reject more early applicants. Suppose that for a recent admissions class, an Ivy League college received 2851 applications for early admission. Of this group, it admitted 1033 students early, rejected 854outright, and deferred 964to the regular admissions pool for further consideration. In the past, this school has admitted 18% of the deferred early admission applicants during the regular admission process. Counting the students admitted early and the students admitted during the regular admission process, the total class size was 2375 Let E,R , and D represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool. If your answer is zero, enter "". a. Use the data to estimate , , and (to decimals). b. Are events and mutually exclusive? Find (to decimals). c. For the students who were admitted, what is the probability that a randomly selected student was accepted for early admission (to decimals)? d. Suppose a student applies for early admission. What is the probability that the student will be admitted for early admission or be deferred and later admitted during the regular admission process (to decimals)? |
Assume that we have two events, and , that are mutually exclusive. Assume further that we know and . If an amount is zero, enter "". a. What is ? b. What is ? c. A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Do you agree with this statement? Use the probability information in this problem to justify your answer. d. What general conclusion would you make about mutually exclusive and independent events given the results of this problem? |
To better understand how husbands and wives feel about their finances, Money Magazine conducted a national poll of married adults age and older with household incomes of or more (Money website). Consider the following example set of responses to the question, "Who is better at getting deals?"
Round your answers to four decimal places, if necessary. a. Develop a joint probability table and use it to answer the following questions.
b. Construct the marginal probabilities for Who Is Better (I Am, My Spouse, We Are Equal). Comment.
c. Given that the respondent is a husband, what is the probability that he feels he is better at getting deals than his wife? d. Given that the respondent is a wife, what is the probability that she feels she is better at getting deals than her husband? e. Given a response "My spouse" is better at getting deals, what is the probability that the response came from a husband? f. Given a response "We are equal," what is the probability that the response came from a husband? What is the probability that the response came from a wife? | ||||||||||||||||||||||||||||||||||||||||||
A 2008 Pew Research Center survey found that more Americans believe they could give up their televisions than could give up their cell phones (Pew Research website). Assume that the following table represents the joint probabilities of Americans who could give up their television or cell phone. Excel File: data04-37.xlsx
a. What is the probability that a person could give up her cell phone (to decimals)? b. What is the probability that a person who could give up her cell phone could also give up television (to decimals)? c. What is the probability that a person who could not give up her cell phone could give up television (to decimals)? d. Is the probability a person could give up television higher if the person could not give up a cell phone or if the person could give up a cell phone? The probability a person could give up television if they could not give up a cellphone is | |||||||||||||||||||||||||
A consulting firm submitted a bid for a large research project. The firm's management initially felt they had a chance of getting the project. However, the agency to which the bid was submitted subsequently requested additional information on the bid. Past experience indicates that for of the successful bids and of the unsuccessful bids the agency requested additional information. a. What is the prior probability of the bid being successful (that is, prior to the request for additional information) (to decimal)? b. What is the conditional probability of a request for additional information given that the bid will ultimately be successful (to decimals)? c. Compute the posterior probability that the bid will be successful given a request for additional information (to decimals). |
According to a article in
a. What is the probability that the male patient has prostate cancer if the PSA test comes back positive (to decimals)? b. What is the probability that the male patient has prostate cancer if the PSA test comes back negative (to decimals)? c. For older men, the prior probability of having cancer increases. Suppose that the prior probability of the male patient is rather than . What is the probability that the male patient has prostate cancer if the PSA test comes back positive (to decimals)? What is the probability that the male patient has prostate cancer if the PSA test comes back negative (to decimals)? d. What can you infer about the PSA test from the results of parts (a), (b), and (c)? The difference between and in parts (a) and (b) is |
A financial manager made two new investments—one in the oil industry and one in municipal bonds. After a one-year period, each of the investments will be classified as either successful or unsuccessful. Consider the making of the two investments as an experiment. a. How many sample points exist for this experiment? b. Choose a tree diagram.
c. Let and How many sample points exist for ? How many sample points exist for ? d. Identify the sample points in the union of the events (). e. Identify the sample points in the intersection of the events (). f. Are events and mutually exclusive? Explain. |
A study of hospital admissions in New York State found that of the admissions led to treatment-caused injuries. One-seventh of these treatment-caused injuries resulted in death, and one-fourth were caused by negligence. Malpractice claims were filed in one out of cases involving negligence, and payments were made in one out of every two claims. a. What is the probability a person admitted to the hospital will suffer a treatment-caused injury due to negligence (to decimals)? b. What is the probability a person admitted to the hospital will die from a treatmen-caused injury (to decimals)? c. What is the probability a person admitted to the hospital is paid a malpractice claim (to decimals)? |
A large consumer goods company ran a television advertisement for one of its soap products. On the basis of a survey that was conducted, probabilities were assigned to the following events. B The probabilities assigned were , , and a. What is the probability of an individual’s purchasing the product given that the individual recalls seeing the advertisement (to decimal)? Does seeing the advertisement increase the probability that the individual will purchase the product? As a decision maker, would you recommend continuing the advertisement (assuming that the cost is reasonable)? b. Assume that individuals who do not purchase the company’s soap product buy from its competitors. What would be your estimate of the company’s market share (to the nearest whole number)? Would you expect that continuing the advertisement will increase the company's market share? Why or why not? c. The company also tested another advertisement and assigned it values of and . What is for this other advertisement (to decimals)? Which advertisement seems to have had the bigger effect on customer purchases? |
A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records show that of the employees suffered lost-time accidents last year. Management believes that a special safety program will reduce such accidents to during the current year. In addition, it estimates that of employees who had lost-time accidents last year will experience a lost-time accident during the current year. a. What percentage of the employees will experience lost-time accidents in both years (to decimals)? b. What percentage of the employees will suffer at least one lost-time accident over the two-year period (to decimals)? |
An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities. p(High-quality oil) = 0.45 p(medium-quality oil) = 0.20 p(no oil) = 0.35 b. After feet of drilling on the first well, a soil test is taken. The probabilities of finding the particular type of soil identified by the test are given below. p(High-quality oil) = 0.25 p(medium-quality oil) = 0.80 p(no oil) = 0.25 Given the soil found in the test, use Bayes' theorem to compute the following revised probabilities (to decimals). What is the new probability of finding oil (to decimals)? According to the revised probabilities, what is the quality of oil that is most likely to be found? |
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