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Ch04 - Ch 4 Prep Questions - Fundamental Probability Concepts
Analytical Methods for Business (BNAD 277)
University of Arizona
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For an experiment in which a single die is rolled, the sample space may be {1, 1, 2, 3, 4, 5}. True False
The probability of a union of events can be greater than 1. True False
Events are exhaustive if they do not share common outcomes of a sample space. True False
Mutually exclusive events may share common outcomes of a sample space. True False
Mutually exclusive and collectively exhaustive events contain all outcomes of a sample space, and they do not share any common outcomes. True False
The union of two events A and B, denoted by , does not have outcomes from both A and B. True False
The complement of an event A, denoted by AC, within the sample space S, is the event consisting of all outcomes of A that are not in S. True False
The intersection of two events A and B, denoted by A ∩ B, is the event consisting of all outcomes that are in A and B. True False
Subjective probability is assigned to an event by drawing on logical analysis. True False
For two independent events A and B, the probability of their intersection is zero. True False
The total probability rule is useful only when the unconditional probability is expressed in terms of probabilities conditional on two mutually exclusive and exhaustive events. True False
Bayes' theorem uses the total probability rule to update the prior probability of an event that has not been affected by any new evidence. True False
Bayes' theorem is used to update prior probabilities based on the arrival of new relevant information. True False
Combinations are used when the order in which different objects are arranged matters. True False
Permutations are used when the order in which different objects are arranged matters. True False
What is probability? A. Any value between 0 and 1 is always treated as a probability of an event. B. A numerical value assigned to an event that measures the number of its occurrences. C. A value between 0 and 1 assigned to an event that measures the likelihood of its occurrence. D. A value between 0 and 1 assigned to an event that measures the unlikelihood of its occurrence.
For an experiment in which a single die is rolled, the sample space is. A. {1, 1, 3, 4, 5, 6} B. {2, 1, 3, 6, 5, 4} C. {1, 2, 3, 4, 4, 5} D. All of the above
A sample space contains. A. Outcomes of the relevant events B. Several outcomes of an experiment C. All possible outcomes of an experiment D. One of several outcomes of an experiment
What is a simple event? A. An event that contains all outcomes of a sample space B. An event that contains several outcomes of a sample space C. An event that contains only one outcome of a sample space D. All of the above
Which of the following is not an event when considering the sample space of tossing two coins? A. {HH, HT} B. {HH, TT, HT} C. {HH, TT, HTH} D. {HH, HT, TH, TT}
Events are collectively exhaustive if. A. They include all events B. They are included in all events C. They contain all outcomes of an experiment D. They do not share any common outcomes of an experiment
Mutually exclusive events. A. Contain all possible outcomes B. May share common outcomes C. Do not share common outcomes D. Do not contain all possible outcomes
Which of the following are mutually exclusive events of an experiment in which two coins are tossed?
A. {TT, HH} and {TT} B. {HT, TH} and {TH} C. {TT, HT} and (HT} D. (TT, HH} and {TH}
In an experiment in which a coin is tossed twice, which of the following represents mutually exclusive and collectively exhaustive events? A. {TT, HH} and {TT, HT} B. {HT, TH} and {HH, TH} C. {TT, HH} and {TH, HT} D. {TT, HT} and {HT, TH}
A probability based on logical analysis rather than on observation or personal judgment is best referred to as a(n). A. A priori probability B. Empirical probability C. Subjective probability D. None of the above
An analyst believes the probability that U. stock returns exceed long-term corporate bond returns over a 5-year period is based on personal assessment. This type of probability is best characterized as a(n) . A. A priori probability B. Empirical probability C. Objective probability D. Subjective probability
Which of the following represents a subjective probability? A. The probability of rolling a 2 on a single die is 1 in 6. B. Based on a conducted experiment, the probability of tossing a head on an unfair coin is 0. C. A skier believes she has a 10% chance of winning a gold medal. D. Based on past observation, a manager believes there is a 3-in-5 chance of retaining an employee for at least one year.
Which of the following represents an empirical probability? A. The probability of tossing a head on a coin is 0. B. The probability of rolling a 2 on a single die is 1 in 6. C. A skier believes she has a 0 chance of winning a gold medal. D. Based on past observation, a manager believes there is a 3-in-5 chance of retaining an employee for at least one year.
An analyst has a limit order outstanding on a stock. He argues that the probability that the order will execute before the close of trading is 0. Thus, the odds for the order executing before the close of trading are. A. 1 in 4 B. 1 in 5 C. 4 to 1 D. 5 to 1
After extensive research, an analyst asserts that there is an 80% chance that ABC Corporation will beat its EPS forecast. Analogously, the odds for the company beating its EPS forecast are. A. 1 in 4 B. 1 in 1. C. 4 to 1 D. 1 to 1
The odds for encountering rain on a 500-mile car trip are 3 to 1. What is the probability of rain on this trip? A. 0. B. 0. C. 0. D. 0.
The odds against winning $1 in the lottery are 19 to 1. What is the probability of winning $1 in the lottery? A. 0. B. 0. C. 0. D. 0.
An experiment consists of tossing three fair coins. What is the probability of tossing two tails? A. 1/ B. 1/ C. 3/ D. 1/
Let , and. Calculate. A. 0. B. 0. C. 0. D. Not enough information to calculate.
Given an experiment in which a fair coin is tossed three times, the sample space is S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}. Event A is defined as tossing one head (H). What is the event AC and what is the probability of this event? A. AC = {TTT, HHH, HTH}; P(AC) = 0. B. AC = {TTT, THH, HHH, HHT}; P(AC) = 0. C. AC = {TTT, HHH, HHT, HTH, HTT}; P(AC) = 0. D. AC = {TTT, HHT, HTH, THH, HHH}; P(AC) = 0.
Let , and. Calculate. A. 0. B. 0. C. 0. D. Not enough information to calculate.
Alison has all her money invested in two mutual funds, A and B. She knows that there is a 40% chance that fund A will rise in price, and a 60% chance that fund B will rise in price given that fund A rises in price. What is the probability that both fund A and fund B will rise in price? A. 0. B. 0. C. 0. D. 1.
Alison has all her money invested in two mutual funds, A and B. She knows that there is a 40% chance that fund A will rise in price, and a 60% chance that fund B will rise in price given that fund A rises in price. There is also a 20% chance that fund B will rise in price. What is the probability that at least one of the funds will rise in price? A. 0. B. 0. C. 0. D. 0.
Alison has all her money invested in two mutual funds, A and B. She knows that there is a 40% chance that fund A will rise in price, and a 60% chance that fund B will rise in price given that fund A rises in price. There is also a 20% chance that fund B will rise in price. What is the probability that neither fund will rise in price? A. 0. B. 0. C. 0. D. 0.
Find the missing values marked xx and yy in the following contingency table:
A. xx = 72, yy = 79 B. xx = 27, yy = 77 C. xx = 27, yy = 79 D. xx = 72, yy = 77
- The contingency table below provides frequencies for the preferred type of exercise for people under the age of 35 and those 35 years of age or older. Find the probability that an individual prefers running.
A. 0.
B. 0.
C. 0.
D. 0.
- The contingency table below provides frequencies for the preferred type of exercise for people under the age of 35, and those 35 years of age or older. Find the probability that an individual prefers biking given that he/she is 35 years old or older.
A. 0.
B. 0.
C. 0.
D. 0.
- The following probability table shows probabilities concerning Favorite Subject and Gender. What is the probability of selecting an individual who is a female or prefers science?
A. 0.
B. 0.
C. 0.
D. 0.
- The following probability table shows probabilities concerning Favorite Subject and Gender. What is the probability of selecting an individual preferring science given that he/she is a female?
A. 0.
B. 0.
C. 0.
D. 0.
- Exhibit 4-1. Two hundred people were asked if they had read a book in the last month. The accompanying contingency table, cross-classified by age, is produced.
Refer to Exhibit 4-1. The probability that a respondent is at least 30 years old is closest to. A. 0. B. 0. C. 0. D. 0.
- Exhibit 4-2. Mark Zuckerberg, the founder of Facebook, has announced that he will eat meat only from animals that he has killed himself (Vanity Fair, November 2011). Suppose 257 people were asked: "Does the idea of killing your own food appeal to you, or not?" The accompanying contingency table, cross- classified by gender, is produced from the 187 respondents.
Refer to Exhibit 4-2. The probability that a respondent is male and feels that the idea of killing his own food is appealing is closest to. A. 0. B. 0. C. 0. D. 0.
- Exhibit 4-2. Mark Zuckerberg, the founder of Facebook, has announced that he will eat meat only from animals that he has killed himself (Vanity Fair, November 2011). Suppose 257 people were asked: "Does the idea of killing your own food appeal to you, or not?" The accompanying contingency table, cross- classified by gender, is produced from the 187 respondents.
Refer to Exhibit 4-2. Given that the respondent is male, the probability that he feels that the idea of killing his own food is appealing is closest to. A. 0. B. 0. C. 0. D. 0.
- Exhibit 4-3. The 150 residents of the town of Wonderland were asked their age and whether they preferred vanilla, chocolate, or swirled frozen yogurt. The results are displayed next.
Refer to Exhibit 4-3. What is the probability that a randomly selected customer prefers vanilla? A. 0. B. 0. C. 0. D. 0.
- Exhibit 4-3. The 150 residents of the town of Wonderland were asked their age and whether they preferred vanilla, chocolate, or swirled frozen yogurt. The results are displayed next.
Refer to Exhibit 4-3. What is the probability a randomly selected customer prefers chocolate given he or she is at least 25 years old? A. 0. B. 0. C. 0. D. 0.
- Exhibit 4-3. The 150 residents of the town of Wonderland were asked their age and whether they preferred vanilla, chocolate, or swirled frozen yogurt. The results are displayed next.
Refer to Exhibit 4-3. What is the probability a randomly selected customer prefers chocolate swirled yogurt or is at least 25 years old? A. 0. B. 0. C. 0. D. 0.
Let , and. Compute. A. 0. B. 0. C. 0. D. 0.
Let , and. Compute. A. 0. B. 0. C. 0. D. 0.
Let , , and. Compute. A. 0. B. 0. C. 0. D. 0.
Let , and. Compute. A. 0. B. 0. C. 0. D. 0.
How many ways can a committee of four students be selected from a 15-member club? A. 15!/44! B. 15!/(4! × 11!) C. 15 × 14 × 13 D. B and C
How many ways can a potential 4-letter word, whether or not it has a meaning, be created out of 10 available different letters? A. 4 * 3 * 2 * 1 B. 10 * 9 * 8 * 7/(4 * 3 * 2) C. 10 * 9 * 8 * 7 * 6 * 5/(4 * 3 * 2) D. 10 * 9 * 8 * 7
When some objects are randomly selected, which of the following is true? A. The order in which objects are selected matters in combinations. B. The order in which objects are selected does not matter in permutations. C. The order in which objects are selected does not matter in combinations. D. The order in which objects are selected matters in both permutations and combinations.
A small company that manufactures juggling equipment makes seven different types of clubs. The company wants to start an ad campaign that emphasizes the myriad combinations the avid juggler can create with the company's clubs. If a juggler wishes to juggle 4 clubs, each of a different type, how many different combinations of the company's clubs can he or she make? A. 7 B. 28 C. 35 D. 210
Boeing currently produces five models of airplanes for commercial sale. The airline that Lauren works for is rapidly expanding and would like to purchase three airplanes of different models to service various routes. Her job is to analyze which three to buy. How many combinations will she have to analyze? A. 5 B. 10 C. 15 D. 20
How many project teams composed of 5 students can be created out of a class of 10 students? A. 10 B. 50 C. 252 D. 30,
The following table summarizes the ages of the 400 richest Americans. Suppose we select one of these individuals. Find the probability that the selected individual is at least 60 years old.
The following table summarizes the ages of the 400 richest Americans. Suppose we select one of these individuals. Find the probability that the selected individual is less than 80 years old.
An experiment consists of rolling a fair die. Find the probability that we roll a 4 or a 6.
An experiment consists of tossing a fair coin and rolling a fair die. Find the probability that we toss a head and roll a 6.
Exams are approaching and Helen is allocating time to studying for exams. She plays for the very successful women's lacrosse team, and must schedule her studying around lacrosse practices and play-off games. The entire team assumes that the probability of making the play-offs is 50%. Helen feels that with the appropriate preparation, she has a 70% chance of getting an A in Marketing, but this chance decreases to 60% if the lacrosse team makes the play-offs. Find the probability of getting an A in Marketing and making the lacrosse play-offs.
Exams are approaching and Helen is allocating time to studying for exams. She plays for the very successful women's lacrosse team, and must schedule her studying around lacrosse practices and play- off games. She feels that with the appropriate preparation, she has a 70% chance of getting an A in Marketing. She also feels that this chance will decrease to 60% if the lacrosse team makes the play-offs. Are getting an A on the exam and being in the lacrosse play-offs independent events? Show evidence of your response.
Ryan is hoping to attend graduate school next year. Two of the schools he applied to are the University of Utah and Ohio State University. The probability he gets accepted to Utah given he got accepted to Ohio State is 0. The probability he gets accepted to Ohio State is 0. The probability he gets accepted to Utah is 0. What is the probability he gets accepted to Ohio State given he gets accepted to Utah?
Two stocks, A and B, have a historical correlation indistinguishable from zero. The probability that stock A increases next year is 0, and the probability that stock B increases next year is 0. Calculate the probability that A and B both increase next year.
Exhibit 4-4. An investor is keeping a careful eye on the real estate markets in Las Vegas and the Inland Empire. The following are her predictions for the real estate market in 2012.
- With 0 probability, foreclosures will increase in Las Vegas.
- With 0 probability, foreclosures will increase in Las Vegas or the Inland Empire.
- With 0 probability, foreclosures will increase in Las Vegas and the Inland Empire.
Refer to Exhibit 4-4. What is the probability that foreclosures will increase in the Inland Empire?
- Exhibit 4-4. An investor is keeping a careful eye on the real estate markets in Las Vegas and the Inland Empire. The following are her predictions for the real estate market in 2012.
- With 0 probability, foreclosures will increase in Las Vegas.
- With 0 probability, foreclosures will increase in Las Vegas or the Inland Empire.
- With 0 probability, foreclosures will increase in Las Vegas and the Inland Empire.
Refer to Exhibit 4-4. What is the probability that foreclosures will increase in the Inland Empire given that they increased in Vegas?
- Exhibit 4-5. The following contingency table provides frequencies for the preferred type of exercise for people under the age of 35 and those 35 years of age or older. Here xx and yy represent missing values.
Refer to Exhibit 4-5. Compute the probability that an individual is under 35 and prefers running.
103 4-6. In January of 2012, the second stop for a Republican to get votes toward the presidential nomination was at the New Hampshire Primary. The following exhibit shows the votes several candidates received from registered Republicans and Independents.
Source: ABC News
Refer to Exhibit 4-6. Given that a randomly selected voter is not a Republican, what is the probability that he/she voted for Ron Paul? A. 0. B. 0. C. 0. D. 0.
104 4-6. In January of 2012, the second stop for a Republican to get votes toward the presidential nomination was at the New Hampshire Primary. The following exhibit shows the votes several candidates received from registered Republicans and Independents.
Source: ABC News
Refer to Exhibit 4-6. If a randomly selected voter voted for Jon Huntsman, what is the probability he is a Republican?
105 part of pharmaceutical testing for drowsiness as a side effect of a drug, 200 patients are randomly assigned to one of two groups of 100 each. One group is given the actual drug and the other a placebo. The number of people who felt drowsy in the next hour is recorded as:
a. What is the probability that a randomly picked patient in the study feels drowsy in the next hour? b. What is the probability that a randomly picked patient in the study takes the placebo or feels drowsy in the next hour? c. Given that the patient was given the drug, what is the probability that he/she feels drowsy in the next hour? d. Is whether a patient feels drowsy independent of taking the drug? Explain using probabilities.
106 in London, Paris, and New York want diners to experience eating in pitch darkness to heighten their senses of taste and smell (Vanity Fair, December 2011). Suppose 400 people were asked: "If given the opportunity, would you eat at one of these restaurants?" The accompanying contingency table, cross-classified by age, would be produced.
Convert the contingency table to a joint probability table.
Ch04 - Ch 4 Prep Questions - Fundamental Probability Concepts
Course: Analytical Methods for Business (BNAD 277)
University: University of Arizona
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