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

Accepted Answer

B

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

Accepted Answer

The probability of getting a question wrong is 0.5. The probability of getting all five questions wrong is (0.5)^5 = 0.03125. Therefore, the probability of getting at least one question correct is 1 - 0.03125 = 0.96875, which rounds to 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.

Accepted Answer

All the experiments simulate the situation because they all provide a 50% chance for each gender, which matches the assumption that the gender of a baby is a random event with equal probability for male and female.

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

Accepted Answer

The two events are independent because the color of the shirt you pull from your closet does not affect the color of the socks you pull from your sock drawer.

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%

Accepted Answer

The probability of not dying from a fall is 100% minus the probability of dying from a fall, which is 100% - 0.41% = 99.59%.

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

Accepted Answer

The answer of The Venn diagram below depicts gender and...

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

Accepted Answer

The probability of choosing "recreation" is 0.310, which is the highest probability among the given options.

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

Accepted Answer

The probability is calculated based on the given data. If 10% of the students are male and chose "outside employment," then the probability is 0.10.

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

Accepted Answer

Theoretical probability is based on mathematical calculations and assumptions, while empirical probability is based on observed data. In this case, the player has not observed any data, so the probability is 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

Accepted Answer

The probability of choosing "recreation" is 0.25 and the probability of choosing "other" is 0.125. The probability of choosing either "recreation" or "other" is 0.25 + 0.125 = 0.375.

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

Accepted Answer

The probability that one household owns a cat is 0.33. Since the households are selected with replacement, the probability that all three households own a cat is (0.33)^3 = 0.035937, which rounds to 0.04.

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

Accepted Answer

All the statements A, B, and C are true regarding probability.

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

Accepted Answer

The probability that a female college student from the group chose "housework" as their most likely activity on Saturday mornings is 0.163. This is because the table shows that 16.3% of female college students chose "housework" as their most likely activity on Saturday mornings.

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

Accepted Answer

The answer of Use the following information to answer the...

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

Accepted Answer

The probability that a household does not own a dog is 1 - 0.39 = 0.61. The probability that none of the three households own a dog is 0.61^3 = 0.22698. Therefore, the probability that at least one household owns a dog is 1 - 0.22698 = 0.77302, which rounds to 0.77.

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

Accepted Answer

The probability that a household does not own a bird is 1 - 0.07 = 0.93. The probability that none of the three households own a bird is 0.93^3 ≈ 0.80. Therefore, the probability that at least one household owns a bird is 1 - 0.80 = 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.

Accepted Answer

The law of large numbers states that as the number of trials increases, the empirical probability will tend to get closer to the theoretical probability, but it does not guarantee an exact match.

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

Accepted Answer

The answer of Use the following table to answer the...

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

Accepted Answer

Political party affiliation often influences opinions on tax policies, suggesting these events are likely 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

Accepted Answer

The probability of selecting a household with a dog is 0.39. The probability of selecting three households with dogs is 0.39 * 0.39 * 0.39 = 0.06.

Quiz 5: Modeling Variation With Probability

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 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)

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.

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)

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?"

Which of the following statements is not true about probability?

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

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.