Deck 5: Modeling Variation With Probability

Question 1

Use the following information to answer questions . 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
and the selection of a day off is independent.
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.

Answer 1

1/7 + 1/7 = 0.286

Question 2

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.

Answer 2

0.763, 0.001

Question 3

Use the following table to answer questions . A random sample of college students was asked to respond
to a survey about how they spend their free time on a week night. 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 Wednesday
afternoon/evening. The activity choices were homework, housework, outside employment, recreation, or other.
Using this example, state two events that are mutually exclusive.

Answer 3

Various. Any combination of the events "student doing homework - type x" and "student engaged in outside employment - type y".

Question 4

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 do 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 5

A researcher wants to compare experimental results with a theoretical value for the probability of getting a tail on a coin and a 1 on a die. Design an experiment to compare the probabilities. Define which one is theoretical and which one is an empirical probability? Explain.

Question 6

Use the following table to answer questions . A random sample of college students was asked to respond
to a survey about how they spend their free time on a week night. 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 Wednesday
afternoon/evening. The activity choices were homework, housework, outside employment, recreation, or other.
If one person is chosen randomly from the group, what is the probability that the student is female and working at outside employment on a Wednesday afternoon/evening? (round to the nearest thousandth)

Question 7

Use the following table to answer questions . A random sample of college students was asked to respond
to a survey about how they spend their free time on a week night. 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 Wednesday
afternoon/evening. The activity choices were homework, housework, outside employment, recreation, or other.
Compare the probability that a randomly chosen female student was engaged in recreation versus a male student on a Wednesday afternoon/evening. (Round to the nearest thousandth)

Question 8

Use the following table to answer questions . A random sample of college students was asked to respond
to a survey about how they spend their free time on a week night. 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 Wednesday
afternoon/evening. The activity choices were homework, housework, outside employment, recreation, or other.
If one person is chosen randomly from the group, what is the probability that the person was male and doing housework on a Wednesday afternoon/evening? (round to the nearest thousandth)

Question 9

Describe why it is true that people are not good at identifying truly random samples so we need to rely on outside mechanisms. Give an example not mentioned in the text.

Question 10

Use the following information to answer questions . 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
and the selection of a day off is independent.
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 11

Use the following information to answer questions . 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 12

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

Question 13

Use the following information to answer questions . 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
and the selection of a day off is independent.
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 14

Use the following table to answer questions . A random sample of college students was asked to respond
to a survey about how they spend their free time on a week night. 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 Wednesday
afternoon/evening. The activity choices were homework, housework, outside employment, recreation, or other.
If one person is chosen randomly from the group, what is the probability that the person was either doing homework or outside employment on a Wednesday afternoon/evening? (round to the nearest thousandth)

Question 15

Use the following information to answer questions . 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 16

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 17

Use the following table to answer questions . A random sample of college students was asked to respond
to a survey about how they spend their free time on a week night. 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 Wednesday
afternoon/evening. The activity choices were homework, housework, outside employment, recreation, or other.
If one person is chosen randomly from the group, what is the probability that the person is working on their homework on a Wednesday afternoon/evening? (round to the nearest thousandth)

Question 18

Use the following information to answer questions . 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 19

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 20

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 21

Use the following table to answer questions . A random sample of car buyers was asked to respond to asurvey about what was the most important quality of the car they purchased. This question is summarized in the table below. The important contributors were fuel efficiency, looks, manufacturer reputation, price or other.
If one car buyer is randomly chosen from the group, what is the probability that the buyer is male and chose "manufacturer reputation" as their most important factor for the purchase?

A)0.208
B)0.100
C)0.230
D)0.130

Question 22

Use the following table to answer questions . A random sample of car buyers was asked to respond to asurvey about what was the most important quality of the car they purchased. This question is summarized in the table below. The important contributors were fuel efficiency, looks, manufacturer reputation, price or other.
If one car buyer is randomly chosen from the group, what is the probability that the buyer is female?

A)0.50
B)0.48
C)0.52
D)0.38

Question 23

Use the following table to answer questions . A random sample of car buyers was asked to respond to asurvey about what was the most important quality of the car they purchased. This question is summarized in the table below. The important contributors were fuel efficiency, looks, manufacturer reputation, price or other.
If one car buyer is randomly chosen from the group, what is the probability that the buyer is female and chose "fuel efficiency" or "other" as their most important factor for the purchase?

A)0.212
B)0.110
C)0.300
D)0.173

Question 24

Use the following information and Venn diagram to answer questions . A survey of 64 members of a UFO
club revealed the following information:
45 believe that we never landed on the moon
49 believe that they have been abducted by space aliens
42 believe both of these things
The Venn diagram below helps depict these data.
Let U be the set of people who were surveyed. Let E be the set of people who believe that we never landed on the
moon. Let A be the set of people who believe that they have been abducted by space aliens. Then we have the
following Venn diagram showing the relationship between sets E, A and U:
How many believe that we never landed on the moon but that they have not been abducted by space aliens?

A)3
B)7
C)12
D)42

Question 25

Which of the following are mutually exclusive events?

A)A car buyer is female and a car buyer chose "looks" as their most important factor for their purchase.
B)A car buyer is male and a car buyer chose "manufacturer reputation" as their most important factor for their purchase.
C)A car buyer is female and a car buyer chose "fuel efficiency" as their most important factor for their purchase.
D)A car buyer chose "fuel efficiency" and "other" as their most important factor for their purchase.

Question 26

Use the following information to answer questions . Suppose that a recent poll of American households about
car ownership found that for households with a car, 39% owned a sedan, 33% owned a van, and 7% owned a sports
car. Suppose that three households are selected randomly and with replacement.
What is the probability that none of the three randomly selected households own a van? (Round to the nearest thousandth)

A)0.699
B)0.060
C)0.036
D)0.301

Question 27

Is the following an example of theoretical probability or empirical probability? A survey was conducted to determine a group of elderly adults' favorite breeds of dogs. He concludes that the probability that the elderly adults prefer a poodle is about 30%.

A)Theoretical
B)Empirical

Question 28

Use your intuition to decide whether the following two events are likely to be independent or associated. Event A: Drawing a club from a deck of cards. Event B: Drawing a card with a black symbol from a deck of cards.

A)Associated
B)Independent

Question 29

Is the following an example of theoretical probability or empirical probability? Joyce and Joel roll two dice 50 times and record their results in the accompanying chart. They calculate the number of times 7 was rolled. This is an example of what type of probability?

A)Theoretical
B)Empirical

Question 30

Use the following table to answer questions . A random sample of car buyers was asked to respond to asurvey about what was the most important quality of the car they purchased. This question is summarized in the table below. The important contributors were fuel efficiency, looks, manufacturer reputation, price or other.
Find the probability of those car buyers who chose "looks" as their most important factor was a female car buyer?

A)0.160
B)0.469
C)0.531
D)0.163

Question 31

Which of the following statements are not true about probability in general?

A)Probability is used to measure the likelihood of random events.
B)Probabilities are always numbers between -1 and 1 inclusive.
C)Probability describes the long-term proportion with which a certain outcome will occur.
D)All of the above are true statements

Question 32

Use your intuition to decide whether the following two events are likely to be independent or associated. Event A: You roll a number larger than four on a die. Event B: Rolling a six on a die.

A)Associated
B)Independent

Question 33

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

A)If you repeat a random experiment many, many times, your outcomes should on average approach the theoretical average.
B)If you repeat a random experiment many, many times, your outcomes should be a unique value that is separate from the theoretical average.
C)If you simulate or conduct an experiment or simulation enough times the empirical probability observed will always match the theoretical probability that is expected.
D)If an experiment with a random outcome is repeated a large number of times, the empirical probability that is observed is consistently different from the theoretical probability.

Question 34

Use the following information to answer questions . Suppose that a recent poll of American households about
car ownership found that for households with a car, 39% owned a sedan, 33% owned a van, and 7% owned a sports
car. Suppose that three households are selected randomly and with replacement.
What is the probability that all three randomly selected households own a van? (Round to the nearest thousandth)

A)0.059
B)0.036
C)0.003
D)0.964

Question 35

Use the following table to answer questions . A random sample of car buyers was asked to respond to asurvey about what was the most important quality of the car they purchased. This question is summarized in the table below. The important contributors were fuel efficiency, looks, manufacturer reputation, price or other.
If one car buyer is randomly chosen from the group, what is the probability that the buyer chose a car based on "looks" as their most important factor for the purchase?

A)0.320
B)0.235
C)0.160
D)0.640

Question 36

Use the following table to answer questions . A random sample of car buyers was asked to respond to asurvey about what was the most important quality of the car they purchased. This question is summarized in the table below. The important contributors were fuel efficiency, looks, manufacturer reputation, price or other.
If one car buyer is randomly chosen from the group, what is the probability amongst female buyers that they chose "price" as their most important factor for the purchase?

A)0.629
B).0.240
C)0.310
D)0.375

Question 37

Use the following information to answer questions . Suppose that a recent poll of American households about
car ownership found that for households with a car, 39% owned a sedan, 33% owned a van, and 7% owned a sports
car. 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 sports car? (Round to the nearest thousandth)

A)0.200
B)0.800
C)0.627
D)0.003

Question 38

The Social Security Administration reported in 2014 that if you are a 70 year old man, there is a 65.8% chance of making it to your 80th birthday. What is the probability that you will die before reaching your 80th birthday? (round to the nearest hundredth place)

A)0.34%
B)0.66%
C)34.20%
D)Can't be determined with the given information.

Question 39

Use the following information and Venn diagram to answer questions . A survey of 64 members of a UFO
club revealed the following information:
45 believe that we never landed on the moon
49 believe that they have been abducted by space aliens
42 believe both of these things
The Venn diagram below helps depict these data.
Let U be the set of people who were surveyed. Let E be the set of people who believe that we never landed on the
moon. Let A be the set of people who believe that they have been abducted by space aliens. Then we have the
following Venn diagram showing the relationship between sets E, A and U:
How many believe neither of these things (that we never landed on the moon and that they have been abducted by space aliens)?

A)42
B)7
C)12
D)3

Question 40

A certain baseball player has a hit 10 times in every 30 times at bat on average. Assume that having a hit is a random event. Which of the following experiments would not simulate this situation?

A)Choose the first 30 digits from a row in the random number table.Designate odd numbers to mean "hit" and even numbers to mean "non-hit".
B)Flip a coin thirty times.Designate a head to mean "hit" and a tail to mean "non-hit".
C)All of the above will simulate the number of hits.
D)None of the above will simulate the number of hits.

Question 41

Use the following table to answer questions ). A random sample of adults was asked to respond to a
survey about whether they use their cell phones to shop for a specific item. One question, summarized in the table
below reflecting probabilities, asked each respondent to choose whether or not they use a cell phone app to shop.
The major age groupings were under 40 or 40 years or older.
What type of probability is the 0.30 shown in the table?

A)Theoretical
B)Empirical

Question 42

Use the following information to answer questions . Suppose that a recent poll of American households
about pet ownership found that for households with pets, 45% owned a dog, 34% owned a cat, and 10% owned a
bird. Suppose that three households are selected randomly and with replacement and the ownership is mutually
exclusive.
What is the probability that none of the three randomly selected households own a cat? (Round to the nearest hundredth)

A)0.17
B)0.96
C)0.71
D)0.29

Question 43

Use the following information to answer questions . Suppose that a recent poll of American households
about pet ownership found that for households with pets, 45% owned a dog, 34% owned a cat, and 10% owned a
bird. Suppose that three households are selected randomly and with replacement and the ownership is mutually
exclusive.
What is the probability that all three randomly selected households own a dog? (Round to the nearest hundredth)

A)0.91
B)0.09
C)0.80
D)0.04

Question 44

Use the following information to answer questions . Suppose that a recent poll of American households
about pet ownership found that for households with pets, 45% owned a dog, 34% owned a cat, and 10% owned a
bird. Suppose that three households are selected randomly and with replacement and the ownership is mutually
exclusive.
What is the probability that at least one of the three randomly selected households own a bird? (Round to the nearest hundredth)

A)0.08
B)0.92
C)0.73
D)0.27

Question 45

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)Flip a coin twenty times.Designate a head to mean "female" and a tail to mean "male".
B)Roll a die twenty times.Designate a 1, 2, or 3 to mean "female" and a 4, 5, or 6 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 the above will simulate the gender of twenty babies.

Question 46

Use the following table to answer questions ). A random sample of adults was asked to respond to a
survey about whether they use their cell phones to shop for a specific item. One question, summarized in the table
below reflecting probabilities, asked each respondent to choose whether or not they use a cell phone app to shop.
The major age groupings were under 40 or 40 years or older.
Find the probability that an adult randomly chosen from the group uses a cell phone app to shop? (round to the nearest thousandth)

A)60%
B)50%
C)40%
D)0.50%

Question 47

Which of the following statements is not true about probability?

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

Question 48

A study asks a sample of adults whether they prefer cats or dogs or neither. Only one answer is allowed. Survey also records whether male or female. Which of the following are mutually exclusive events in this study?

A)Adult is male and adult prefers neither cats nor dogs.
B)Adult is female and likes dogs.
C)Adult is male and likes cats and dogs.
D)Adult is female and prefers cats.

Question 49

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)Associated
B)Independent

Question 50

A six-sided die is rolled and a coin is tossed. The probability of getting a tail on the coin and a 2 on the die is 8.3%. Is this an example of a theoretical or empirical probability?

A)Theoretical
B)Empirical

Question 51

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

Question 52

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

A)The LLN is almost always true, but there are special occasions, even when outcomes are random, when the LLN can be broken.
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 you simulate or conduct an experiment or simulation enough times the empirical probability observed will always match the theoretical probability that is expected.
D)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.

Question 53

Use the following table to answer questions ). A random sample of adults was asked to respond to a
survey about whether they use their cell phones to shop for a specific item. One question, summarized in the table
below reflecting probabilities, asked each respondent to choose whether or not they use a cell phone app to shop.
The major age groupings were under 40 or 40 years or older.
Which of the following are mutually exclusive events in this study?

A)Adults over 40 years of age and uses a cell phone app for shopping.
B)Adult is over 40 years of age and does not use a cell phone app for shopping.
C)Adult is under 40 years of age and does not use a cell phone app for shopping.
D)None of these choices.

Question 54

Use the following table to answer questions ). A random sample of adults was asked to respond to a
survey about whether they use their cell phones to shop for a specific item. One question, summarized in the table
below reflecting probabilities, asked each respondent to choose whether or not they use a cell phone app to shop.
The major age groupings were under 40 or 40 years or older.
If one adult is randomly chosen from the group, what is the probability that if the adult does not use a cell phone app for shopping and is over 40 years old?

A)40%
B)30%
C)60%
D)70%

Question 55

Use the following table to answer questions ). A random sample of adults was asked to respond to a
survey about whether they use their cell phones to shop for a specific item. One question, summarized in the table
below reflecting probabilities, asked each respondent to choose whether or not they use a cell phone app to shop.
The major age groupings were under 40 or 40 years or older.
If one adult is randomly chosen from the group, what is the probability that the adult is 40 years or older?

A)40%
B)0.40%
C)60%
D)50%

Question 56

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

Question 57

A homeowner notices that 8 out of 14 days the mail arrives before 3pm. She concludes that the probability that the mail will arrive before 3pm tomorrow is about 57%. Is this an example of a theoretical or empirical probability?

A)Theoretical
B)Empirical

Question 58

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)Associated
B)Independent

Question 59

Use the following table to answer questions ). A random sample of adults was asked to respond to a
survey about whether they use their cell phones to shop for a specific item. One question, summarized in the table
below reflecting probabilities, asked each respondent to choose whether or not they use a cell phone app to shop.
The major age groupings were under 40 or 40 years or older.
If one adult is randomly chosen from the group, what is the probability that the adult uses a cell phone app for shopping and is under 40 years of age?

A)40%
B)10%
C)60%
D)30%

Question 60

Use the following information to answer questions . Suppose that a recent poll of American households
about pet ownership found that for households with pets, 45% owned a dog, 34% owned a cat, and 10% owned a
bird. Suppose that three households are selected randomly and with replacement and the ownership is mutually
exclusive.
What is the probability that at least two of the three randomly selected households own either a cat or a dog? (Round to the nearest hundredth)

A)0.97
B)0.89
C)0.06
D)0.94