Deck 5: Modeling Variation With Probability

Question 1

The Venn diagram below depicts gender and occupation of a sample of adults. Which region on the Venn diagram represents the event "The individual is a female firefighter?"

A)Region 3
B)Region 4
C)Region 1
D)Region 2

Answer 1

Region 4

Question 2

A true/false pop quiz contains five questions. What is the probability that when guessing, a student will get at least one question correct? (Round to the nearest hundredth)

A)0.76
B)1.00
C)0.50
D)0.97

Answer 2

0.97

Question 3

Use the following table to answer the question. A random sample of college students was asked to respond to a survey about how they spend their free time on weekends. One question, summarized in the table below, asked each respondent to choose the one activity that they are most likely to participate in on a Saturday morning. The activity choices were homework, housework, outside employment, recreation, or other.

If 20 babies are born, how often are there 12 or more female babies? Assume that the gender of a baby is a random event. Which of the following experiments would not simulate this situation?

A)Roll a die twenty times. Designate a 1, 2, or 3 to mean "female" and a 4, 5, or 6 to mean "male."
B)Flip a coin twenty times. Designate a head to mean "female" and a tail to mean "male."
C)Choose the first twenty digits from a row in the random number table. Designate odd numbers to mean "female" and even numbers to mean "male."
D)All of these will simulate the gender of twenty babies.

Answer 3

All of these will simulate the gender of twenty babies.

Question 4

Use your intuition to decide whether the following two events are likely to be independent or associated. Event A: You reach into your dark closet, without looking, and pull out a black shirt. Event B: You reach into your sock drawer, without looking, and pull out black socks.

A)Associated
B)Independent

Question 5

The National Center for Health Statistics has found that there is a 0.41% chance that an American citizen will die from falling. What is the probability that you will not die from a fall? (Round to the nearest hundredth of a percent)

A)99.59%
B)Can't be determined with the given information.
C)93.31%
D)59.00%

Question 6

The Venn diagram below depicts gender and occupation of a sample of adults. Which region on the Venn diagram represents the event "The individual is a male nurse?"

A)Region 2
B)Region 4
C)Region 3
D)Region 1

Question 7

Use the following table to answer the question. A random sample of college students was asked to respond to a survey about how they spend their free time on weekends. One question, summarized in the table below, asked each respondent to choose the one activity that they are most likely to participate in on a Saturday morning. The activity choices were homework, housework, outside employment, recreation, or other.

If one student is randomly chosen from the group, what is the probability that the student chose "recreation" as their most likely activity on a Saturday morning?

A)0.310
B)0.115
C)0.195
D)None of these

Question 8

Use the following table to answer the question. A random sample of college students was asked to respond to a survey about how they spend their free time on weekends. One question, summarized in the table below, asked each respondent to choose the one activity that they are most likely to participate in on a Saturday morning. The activity choices were homework, housework, outside employment, recreation, or other.

If one student is randomly chosen from the group, what is the probability that the student is male and chose "outside employment" as their most likely activity on a Saturday morning?

A)0.23
B)0.13
C)0.10
D)None of these

Question 9

Is the following an example of theoretical probability or empirical probability? At a carnival shell game the player can pay three dollars and choose the shell that he or she believes is hiding the prize. There are four shells that are thoroughly mixed up after each guess. The player concludes that there is a one in four chance of randomly picking the winning shell.

A)Empirical
B)Theoretical

Question 10

Use the following table to answer the question. A random sample of college students was asked to respond to a survey about how they spend their free time on weekends. One question, summarized in the table below, asked each respondent to choose the one activity that they are most likely to participate in on a Saturday morning. The activity choices were homework, housework, outside employment, recreation, or other.

If one student is randomly chosen from the group, what is the probability that the student chose "recreation" or "other" as their most likely activity on a Saturday morning?

A)0.375
B)0.275
C)0.395
D)None of these

Question 11

Use the following information to answer the question. Suppose that a recent poll of American households about pet ownership found that for households with a pet, 39% owned exactly a dog, 33% owned a cat, and 7% owned a bird. Suppose that three households are selected randomly and with replacement.
What is the probability that all three randomly selected households own a cat? (Round to the nearest hundredth)

A)0.03
B)0.04
C)0.06
D)None of these

Question 12

Which of the following statements is not true about probability?

A)Probability is used to measure how often random events occur.
B)A probability of 0 means that an event will not occur, and a probability of 1 means that an event is certain to occur.
C)Probabilities are always numbers between 0 and 1 inclusive.
D)All of these are true statements

Question 13

Use the following table to answer the question. A random sample of college students was asked to respond to a survey about how they spend their free time on weekends. One question, summarized in the table below, asked each respondent to choose the one activity that they are most likely to participate in on a Saturday morning. The activity choices were homework, housework, outside employment, recreation, or other.

Find the probability that a female college student from the group chose "housework" as their most likely activity on Saturday mornings? (Round to the nearest thousandth)

A)0.163
B)0.531
C)0.520
D)None of these

Question 14

Use the following information to answer the question. Suppose that a recent poll of American households about pet ownership found that for households with one pet, 39% owned a dog, 33% owned a cat, and 7% owned a bird. Suppose that three households are selected randomly and with replacement.
What is the probability that none of the three randomly selected households own a cat? (Round to the nearest hundredth)

A)0.46
B)0.30
C)0.70
D)None of these

Question 15

Use the following information to answer the question. Suppose that a recent poll of American households about pet ownership found that for households with a pet, 39% owned exactly a dog, 33% owned a cat, and 7% owned a bird. Suppose that three households are selected randomly and with replacement.
What is the probability that at least one of the three randomly selected households own a dog? (Round to the nearest hundredth)

A)0.27
B)0.61
C)0.77
D)0.70

Question 16

Use the following information to answer the question. Suppose that a recent poll of American households about pet ownership found that for households with one pet, 39% owned a dog, 33% owned a cat, and 7% owned a bird. Suppose that three households are selected randomly and with replacement.
What is the probability that at least one of the three randomly selected households own a bird? (Round to the nearest hundredth)

A)0.60
B)0.80
C)0.40
D)0.20

Question 17

Which of the following statements is true about the "law of large numbers" (LLN)?

A)The LLN states that if an experiment with a random outcome is repeated a large number of times, the empirical probability that is observed is likely to be close to the theoretical probability.
B)The LLN states that if you simulate or conduct an experiment or simulation enough times the empirical probability observed will always match the theoretical probability that is expected.
C)The LLN is almost always true, but there are special occasions, even when outcomes are random, when the LLN can be broken.
D)The LLN states that the empirical probability that is observed will simulate the theoretical probability that is expected for any finite number of trials, so a simulation or experiment need not have an excessive number of trials.

Question 18

Use the following table to answer the question. A random sample of college students was asked to respond to a survey about how they spend their free time on weekends. One question, summarized in the table below, asked each respondent to choose the one activity that they are most likely to participate in on a Saturday morning. The activity choices were homework, housework, outside employment, recreation, or other.

If one student is randomly chosen from the group, what is the probability that the student chose "outside employment" as their most likely activity on a Saturday morning?

A)0.43
B)0.13
C)0.23
D)None of these

Question 19

Use your intuition to decide whether the following two events are likely to be independent or associated. Even A: A randomly selected registered voter's political party affiliation is Republican Event B: A randomly selected registered voter opposes a new tax on fuel.

A)Independent
B)Associated

Question 20

Use the following information to answer the question. Suppose that a recent poll of American households about pet ownership found that for households with one pet, 39% owned a dog, 33% owned a cat, and 7% owned a bird. Suppose that three households are selected randomly and with replacement.
What is the probability that all three randomly selected households own a dog? (Round to the nearest hundredth)

A)0.06
B)0.39
C)0.23
D)None of these

Question 21

Use the following table to answer the question. A random sample of college students was asked to respond to a survey about how they spend their free time on weekends. One question, summarized in the table below, asked each respondent to choose the one activity that they are most likely to participate in on a Saturday morning. The activity choices were homework, housework, outside employment, recreation, or other.

Which of the following are mutually exclusive events?

A)Student is male and student chose "outside employment" as their most likely activity on Saturday mornings.
B)Student is male and student chose "housework" as their most likely activity on Saturday mornings.
C)Student is female and student chose "housework" as their most likely activity on Saturday mornings.
D)Student chose "recreation" and student chose "other" as their most likely activity on Saturday mornings.

Question 22

Use your intuition to decide whether the following events are likely to be independent or associated. Event A: The randomly selected carton of milk you purchased from the store is sour. Event B: Your car won't start on a randomly selected morning.

A)Independent
B)Associated

Question 23

Use the following table to answer the question. A random sample of college students was asked to respond to a survey about how they spend their free time on weekends. One question, summarized in the table below, asked each respondent to choose the one activity that they are most likely to participate in on a Saturday morning. The activity choices were homework, housework, outside employment, recreation, or other.

If one student is randomly chosen from the group, what is the probability that the student chose "homework" or "housework" as their most likely activity on a Saturday morning?

A)0.075
B)0.395
C)0.145
D)None of these

Question 24

Find the probability that a male college student from the group chose "housework" as their most likely activity on Saturday mornings? (Round to the nearest thousandth)

A)0.302
B)0.145
C)0.156
D)None of these

Question 25

Use your intuition to decide whether the following events are likely to be independent or associated. Event A: A randomly selected person is married with no children. Event B: A randomly selected person opposes a tax credit for children.

A)Independent
B)Associated

Question 26

Use the following information to answer the question. Suppose that a recent poll of American households about pet ownership found that for households with a pet, 39% owned exactly a dog, 33% owned a cat, and 7% owned a bird. Suppose that three households are selected randomly and with replacement.
What is the probability that none of the three randomly selected households own a bird? (Round to the nearest hundredth)

A)0.86
B)0.80
C)0.93
D)None of these

Question 27

Which of the following statements is true about the Law of Large Numbers (LLN)?

A)The LLN states that if you simulate or conduct an experiment or simulation enough times the empirical probability observed will always match the theoretical probability that is expected.
B)The LLN states that the empirical probability that is observed will simulate the theoretical probability that is expected for any finite number of trials, so a simulation or experiment need not have an excessive number of trials.
C)The LLN states that if an experiment with a random outcome is repeated a large number of times, the empirical probability that is observed is likely to be close to the theoretical probability.
D)The LLN is almost always true, but there are special occasions, even when outcomes are random, when the LLN can be broken.

Question 28

Use the following table to answer the question. A random sample of college students was asked to respond to a survey about how they spend their free time on weekends. One question, summarized in the table below, asked each respondent to choose the one activity that they are most likely to participate in on a Saturday morning. The activity choices were homework, housework, outside employment, recreation, or other.

Which of the following are mutually exclusive events?

A)Student is female and student chose "outside employment" as their most likely activity on Saturday mornings.
B)Student is female and student chose "housework" as their most likely activity on Saturday mornings.
C)Student is male and student chose "housework" as their most likely activity on Saturday mornings.
D)Student chose "outside employment" and student chose "other" as their most likely activity on Saturday mornings.

Question 29

Use the following table to answer the question. A random sample of college students was asked to respond to a survey about how they spend their free time on weekends. One question, summarized in the table below, asked each respondent to choose the one activity that they are most likely to participate in on a Saturday morning. The activity choices were homework, housework, outside employment, recreation, or other.

If one student is randomly chosen from the group, what is the probability that the student is male?

A)0.52
B)0.48
C)0.50
D)None of these

Question 30

Use the following table to answer the question. A random sample of college students was asked to respond to a survey about how they spend their free time on weekends. One question, summarized in the table below, asked each respondent to choose the one activity that they are most likely to participate in on a Saturday morning. The activity choices were homework, housework, outside employment, recreation, or other.

If one student is randomly chosen from the group, what is the probability that the student is female or chose "homework" as their most likely activity on a Saturday morning?

A)0.755
B)0.900
C)0.665
D)None of these

Question 31

Use the following table to answer the question. A random sample of college students was asked to respond to a survey about how they spend their free time on weekends. One question, summarized in the table below, asked each respondent to choose the one activity that they are most likely to participate in on a Saturday morning. The activity choices were homework, housework, outside employment, recreation, or other.

What is the probability that a randomly chosen survey respondent is male or chose "recreation" as their most likely activity on Saturday mornings?

A)0.675
B)0.480
C)0.790
D)None of these

Question 32

Use the following table to answer the question. A random sample of college students was asked to respond to a survey about how they spend their free time on weekends. One question, summarized in the table below, asked each respondent to choose the one activity that they are most likely to participate in on a Saturday morning. The activity choices were homework, housework, outside employment, recreation, or other.

If one student is randomly chosen from the group, what is the probability that the student is female?

A)0.50
B)0.52
C)0.48
D)None of these

Question 33

Is the following an example of theoretical probability or empirical probability? A card player declares that there is a one in thirteen chance that the next card pulled from a well- shuffled, full deck will be a queen.

A)Empirical
B)Theoretical

Question 34

Which of the following statements is not true about probability?

A)Probabilities are always numbers between 0 and 1 inclusive.
B)A probability of zero means that an event will not happen, a probability of one means that an event is certain to happen.
C)Probability is used to measure how often random events occur.
D)All of these are true statements

Question 35

Use the following table to answer the question. A random sample of college students was asked to respond to a survey about how they spend their free time on weekends. One question, summarized in the table below, asked each respondent to choose the one activity that they are most likely to participate in on a Saturday morning. The activity choices were homework, housework, outside employment, recreation, or other.

If one student is randomly chosen from the group, what is the probability that the student is female and chose "outside employment" as their most likely activity on a Saturday morning?

A)0.23
B)0.13
C)0.43
D)None of these

Question 36

Is the following an example of theoretical probability or empirical probability? A fisherman notes that eight out of ten times that he uses a certain lure he catches a fish within an hour. He concludes that the probability that the lure will catch a fish on his fishing next trip is about 80%

A)Empirical
B)Theoretical

Question 37

A true/false pop quiz contains seven questions. What is the probability that when guessing, a student will get at least one question correct? (Round to the nearest hundredth)

A)1.00
B)0.50
C)0.97
D)0.99

Question 38

The National Center for Health Statistics has found that there is a 5.01% chance that an American citizen will die from an accident (unintentional injury). What is the probability that you will not die from an accident? (Round to the nearest hundredth of a percent)

A)99.50%
B)94.99%
C)95.00%
D)Can't be determined with the given information.

Question 39

Use the following table to answer the question. A random sample of college students was asked to respond to a survey about how they spend their free time on weekends. One question, summarized in the table below, asked each respondent to choose the one activity that they are most likely to participate in on a Saturday morning. The activity choices were homework, housework, outside employment, recreation, or other.

If 20 babies are born, how often are there 8 or less male babies? Assume that the gender of a baby is a random event. Which of the following experiments would not simulate this situation?

A)Roll a die twenty times. Designate a 1, 2, or 3 to mean "female" and a 4, 5, or 6 to mean "male."
B)Flip a coin twenty times. Designate a head to mean "female" and a tail to mean "male."
C)Choose the first twenty digits from a row in the random number table. Designate odd numbers to mean "female" and even numbers to mean "male."
D)All of these will simulate the gender of twenty babies.

Question 40

Is the following an example of theoretical probability or empirical probability? A homeowner notes that five out of seven days the newspaper arrives before 5 pm. He concludes that the probability that the newspaper will arrive before 5 pm tomorrow is about 71%.

A)Theoretical
B)Empirical

Question 41

Use the following table to answer the question. A random sample of 200 new vehicle buyers were asked to respond to a survey about what kind of vehicle they purchased. One question, summarized in the table below, asked each respondent to choose the vehicle that best described the type of vehicle that they purchased. The vehicle choices were car, pick
sport utility vehicle, van, or other.

If one person is chosen randomly from the group, what is the probability that the person is female?

Question 42

A card player claims that the probability of choosing a red jack from a well- shuffled deck of cars is 1/26 because choosing any card is equally likely and there are two red jacks in the deck of fifty- two cards. Is this an example of a theoretical probability or an empirical probability? Explain.

Question 43

Use the following information to answer the question. Suppose that the typical work schedule for the wait staff at Sam's BBQ Shack, which is open seven days a week, is five days on with two days off each week. A week begins on Monday and ends on Sunday. Assume that any day of the week is equally likely to be a day off.
What is the probability that Isaac, a waiter at Sam's BBQ Shack, will have Saturday or Sunday off? Show your work and round to the nearest tenth of a percent.

Question 44

Use the following information to answer the question. Suppose that a recent poll of single people over the age of thirty- five were asked about their living arrangements. The poll found that 34% rented a house or apartment, 21% owned a house, and 17% owned a condominium. Suppose that four single people are selected randomly and with replacement.
What is the probability that none of the four randomly selected people rent a house or apartment? Show your work and round to the nearest thousandth.

Question 45

Use your intuition and state whether these two events are likely to be associated or independent. Explain.
Event A: A randomly selected adult is a pet owner.
Event B: A randomly selected adult responds favorably to the survey question "Should a portion of the beach be set aside as an (unleashed)dog beach?"

Question 46

Describe the difference between a theoretical probability and an empirical probability. Give at least one example of each type of probability.

Question 47

Use the following information to answer the question. Suppose that the typical work schedule for the wait staff at Sam's BBQ Shack, which is open seven days a week, is five days on with two days off each week. A week begins on Monday and ends on Sunday. Assume that any day of the week is equally likely to be a day off.
What is the probability that Issac will have Saturday and Sunday off? Show your work and round to the nearest tenth of a percent.

Question 48

Use the following information to answer the question. Suppose that the typical work schedule for the wait staff at Sam's BBQ Shack, which is open seven days a week, is five days on with two days off each week. A week begins on Monday and ends on Sunday. Assume that any day of the week is equally likely to be a day off.
State the complement of the event given in question (5)and calculate the probability of the complement. Show your work and round to the nearest tenth of a percent.

Question 49

Use the following table to answer the question. A random sample of 200 new vehicle buyers were asked to respond to a survey about what kind of vehicle they purchased. One question, summarized in the table below, asked each respondent to choose the vehicle that best described the type of vehicle that they purchased. The vehicle choices were car, pick- up truck, sport utility vehicle, van, or other.

If one person is chosen randomly from the group, what is the probability that the person purchased a van?

Question 50

A multiple choice quiz contains five questions. Each question has four answer choices. Michael is not prepared for the quiz and decides to guess for each question. What is the probability that Michael will get at least one question correct? What is the probability that Michael will get all five questions correct? Show your work and round to the nearest thousandth.

Question 51

Jody flips a coin ten times and observes the outcome of heads three times. Yvonne flips a coin one hundred times and observes the outcome of heads forty- eight times. Jody states that his coin must not be fair because so few heads were observed. Pretend you are Yvonne and explain to Jody why his results does not indicate that he has an unfair coin by explaining to him what the Law of Large Numbers is, and how it justifies the results that were observed in both experiments.

Question 52

Use the following table to answer the question. A random sample of 200 new vehicle buyers were asked to respond to a survey about what kind of vehicle they purchased. One question, summarized in the table below, asked each respondent to choose the vehicle that best described the type of vehicle that they purchased. The vehicle choices were car, pick- up truck, sport utility vehicle, van, or other.

If one person is chosen randomly from the group, what is the probability that the person purchased a sport utility vehicle or a pick- up truck?

Question 53

Suppose you would like a mug of hot chocolate with cinnamon. You reach into the kitchen cupboard containing twenty mixed up mismatched mugs without looking and pull out a pink coffee cup. You also reach into a kitchen drawer containing 30 different mixed up spice jars without looking and pull out the cinnamon. Use your intuition and state whether these two events are associated or independent. Explain.

Question 54

Use the following table to answer the question. A random sample of 200 new vehicle buyers were asked to respond to a survey about what kind of vehicle they purchased. One question, summarized in the table below, asked each respondent to choose the vehicle that best described the type of vehicle that they purchased. The vehicle choices were car, pick- up truck, sport utility vehicle, van, or other.

Find the probability that a randomly chosen female buyer bought a van. (Round to the nearest hundredth)

Question 55

Using this example, state two events that are mutually exclusive.

Question 56

Use the following information to answer the question. Suppose that a recent poll of single people over the age of thirty- five were asked about their living arrangements. The poll found that 34% rented a house or apartment, 21% owned a house, and 17% owned a condominium. Suppose that four single people are selected randomly and with replacement.
What is the probability that all four people rent a house or apartment? Show your work and round to the nearest thousandth.

Question 57

Use the following information to answer the question. Suppose that a recent poll of single people over the age of thirty- five were asked about their living arrangements. The poll found that 34% rented a house or apartment, 21% owned a house, and 17% owned a condominium. Suppose that four single people are selected randomly and with replacement.
What is the probability that at least one of the four randomly selected people rents a house or apartment? Show your work and round to the nearest thousandth.

Question 58

Consider one toss of a fair six- sided die. State the sample space of possible outcomes. State one possible random event then state the theoretical probability of that event. Explain how you know that this is the probability of the random event.

Question 59

Use the following table to answer the question. A random sample of 200 new vehicle buyers were asked to respond to a survey about what kind of vehicle they purchased. One question, summarized in the table below, asked each respondent to choose the vehicle that best described the type of vehicle that they purchased. The vehicle choices were car, pick- up truck, sport utility vehicle, van, or other.

If one person is chosen randomly from the group, what is the probability that the person was male and bought a car?

Question 60

A football game official tosses a coin at the beginning of each game to determine who will have possession of the ball first. In the previous ten games the toss has come up tails four times. The official says the probability that the coin will come up tails again is 40%. Is the official referring to a theoretical probability or an empirical probability? Explain.