Question 1

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?

Accepted Answer

Empirical probability is based on observations or experiments, not on a theoretical model. The 0.30 in the table likely comes from observed data, making it empirical.

Question 2

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)

Accepted Answer

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

Question 3

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)

Accepted Answer

The probability that all three randomly selected households own a dog is calculated by multiplying the probability of one household owning a dog (45% or 0.45) by itself three times (since the selection is with replacement and independent): $0.45 \times 0.45 \times 0.45 = 0.091125$, which rounds to 0.09 or 9%.

Question 4

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)

Accepted Answer

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

Question 5

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?

Accepted Answer

All the options provided simulate a binary outcome with equal probability for each outcome, accurately representing the random event of a baby being male or female.

Question 6

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)

Accepted Answer

The correct answer is 50%, which is represented as choice B. This is because the question asks for the probability in a percentage form, not as a decimal or fraction. Therefore, 50% is the correct choice, and the other options either represent the percentage incorrectly or use a different format (like 0.50% which is actually 0.5%).

Question 7

Which of the following statements is not true about probability?

Accepted Answer

All the statements provided are true regarding the basic principles of probability.

Question 8

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?

Accepted Answer

Mutually exclusive events cannot occur at the same time. An adult cannot like both cats and dogs simultaneously if only one answer is allowed, making option C mutually exclusive.

Question 9

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.

Accepted Answer

Event A (being married with no children) and Event B (opposing a tax credit for children) are likely associated because individuals without children might be more inclined to oppose tax credits that do not benefit them directly, such as a tax credit for children.

Question 10

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?

Accepted Answer

The probability is theoretical because it is calculated based on known outcomes of a fair die and a fair coin, not on experimental or observed results.

Question 11

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"?

Accepted Answer

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

Question 12

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

Accepted Answer

The Law of Large Numbers (LLN) indicates that as the number of trials in an experiment increases, the empirical (observed) probability approaches the theoretical (expected) probability.

Question 13

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?

Accepted Answer

Mutually exclusive events cannot happen at the same time. However, the given options A, B, and C describe different segments of a population based on age and behavior, not events that cannot occur simultaneously for an individual. Therefore, none of these choices are mutually exclusive events.

Question 14

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?

Accepted Answer

Without specific data provided in the question, it's impossible to accurately calculate or determine the probability of an adult not using a cell phone app for shopping and being over 40 years old. Therefore, any choice given here is arbitrary and not based on statistical or factual information.

Question 15

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?

Accepted Answer

The probability is given as 40%, which means that 40% of the adults in the group are 40 years or older.

Question 16

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)

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 17

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?

Accepted Answer

Empirical probability is based on observations or experiments from past events. Since the homeowner is using past data (8 out of 14 days) to estimate the probability, it is an example of empirical probability.

Question 18

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.

Accepted Answer

Events A and B are independent because the sourness of a carton of milk has no relation to whether your car starts on any given morning.

Question 19

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?

Accepted Answer

The probability of choosing an adult who uses a cell phone app for shopping is 40%. The probability of choosing an adult who is under 40 years of age is 60%. The probability of choosing an adult who uses a cell phone app for shopping and is under 40 years of age is 40% * 60% = 24%.

Question 20

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)

Accepted Answer

The probability of selecting a household that owns either a cat or a dog is 45% + 34% = 79%. The probability of at least two out of three households owning either a cat or a dog can be calculated using the binomial probability formula, considering the scenarios where exactly two households or all three households own a cat or a dog. The calculation involves finding the probabilities of these scenarios and adding them together, leading to a result that rounds to 0.89.

Quiz 5: Modeling Variation With Probability