Question 1

A random experiment is a process leading to two or more possible outcomes.

Accepted Answer

A random experiment can have multiple possible outcomes.

Question 2

A subset of the basic outcomes is classified as a sample.

Accepted Answer

A subset of the basic outcomes is classified as an event, not a sample. A sample refers to a subset of items or observations from a larger population, whereas an event is a set of outcomes of a random experiment.

Question 3

Which of the following applications would an auditor apply to determine the probability of a corporation's account balance being in error?

Accepted Answer

Bayes' theorem is used to calculate the probability of an event occurring based on prior knowledge of conditions that might be related to the event. In auditing, Bayes' theorem can be applied to assess the probability of an account balance being in error based on the results of tests performed on the account.

Question 4

An empty set results from mutually exclusive outcomes.

Accepted Answer

Mutually exclusive outcomes mean that the occurrence of one outcome prevents the occurrence of another within the same experiment, but it does not necessarily result in an empty set. An empty set represents a situation where no outcomes are possible or an event that cannot happen, which is different from mutually exclusive outcomes.

Question 5

The probabilities that result from studying two distinct sets of events are called:

Accepted Answer

The probabilities resulting from studying two distinct sets of events are called bivariate probabilities. Bivariate probabilities involve the analysis of the relationship between two variables or sets of events, whereas individual probabilities and classic probabilities are typically used to describe the likelihood of a single event occurring. Problem probabilities is not a commonly used term in probability theory.

Question 6

Classical probability is the proportion of times that an event will occur assuming all outcomes in a sample space have an equal chance to occur.

Accepted Answer

This is the definition of classical probability.

Question 7

The set of all basic outcomes from a random experiment is called the sample space.

Accepted Answer

This is a true statement. The sample space is the set of all possible outcomes from a random experiment, and it forms the basis for calculating probabilities.

Question 8

The result given by the ratio of the probability of an event divided by the probability of its complement is called the:

Accepted Answer

The ratio of the probability of an event to the probability of its complement is called odds in favor of the event. For example, if the probability of an event is 0.3, the probability of its complement is 0.7, and the odds in favor of the event are 0.3/0.7, or approximately 0.43.

Question 9

The use of permutations or combinations is helpful in some cases when computing the probability of an event.

Accepted Answer

Permutations and combinations are mathematical tools that can be used to calculate the probability of particular events. They are particularly useful in situations where the outcomes can be counted in different ways or the order in which the outcomes occur is important. By using permutations or combinations, we can figure out the total number of possible outcomes and then calculate the probability of a given event based on those outcomes.

Question 10

When a problem arises in counting the numbers of basic outcomes in the sample space and the event of interest to compute the probability of an event,it is helpful to use:

Accepted Answer

Permutations and combinations are useful tools for counting the number of basic outcomes in a sample space, especially when the sample space is too large to list or visualize. These techniques are also helpful in counting the number of ways an event of interest can occur. Therefore, using permutations or combinations can aid in computing the probability of an event.

Question 11

The diagram which provides an intuitive understanding of the addition rule which computes the probability of the union of events is called a:

Accepted Answer

A Venn diagram is a visual representation of sets and their relationships. It is often used in probability to understand the addition rule, which computes the probability of the union of events. The diagram provides an intuitive way to understand the concept of adding probabilities of two or more events. The circles in a Venn diagram represent sets, and the overlapping regions indicate the intersection of those sets. By summing the probabilities of the individual events and subtracting the overlap, we can determine the probability of the union of events.

Question 12

Events whose probability of their intersection is the product of their individual probabilities and is more than 0 are called:

Accepted Answer

The property described in the question is a characteristic of independent events. If events A and B are independent, then the probability of both A and B occurring is equal to the product of their individual probabilities: P(A ∩ B) = P(A) × P(B).

Question 13

The application which provides a way of revising conditional probabilities by using available information and provisions for revising conditional probabilities with other information that is useful for management decision making is called:

Accepted Answer

The application described in the question is referring to Bayes' theorem, which provides a way of updating conditional probabilities based on new information. Option A (overinvolvement ratios) is not relevant to the question. Option C (empirical formula) refers to a formula based on observed data rather than conditional probabilities. Option D (probability rules) is too broad and does not specifically address the application described in the question.

Question 14

Business decisions and policies are often based on true sets of probabilities.

Accepted Answer

Business decisions and policies are often based on estimates, assumptions, and models that may not always reflect true probabilities due to uncertainty and incomplete information.

Question 15

If A and B are independent events with P(A)= 0.20 and P(B)= 0.60,then P(A |B)is:

Accepted Answer

Since A and B are independent, the probability of A given B is simply the probability of A, which is 0.20.

Question 16

If A and B are independent events with P(A)= 0.60 and P(B)= 0.70,then the probability that A occurs or B occurs or both occur is:

Accepted Answer

When dealing with the probability of A or B or both occurring, we use the addition rule for independent events: P(A or B) = P(A) + P(B) - P(A and B). Since A and B are independent, P(A and B) = P(A) * P(B) = 0.60 * 0.70 = 0.42. Therefore, P(A or B) = 0.60 + 0.70 - 0.42 = 0.88. Thus, the best choice is B with a probability of 0.88.

Question 17

The probabilities that may be computed by summing the corresponding row or column of a two-way table are called:

Accepted Answer

Marginal probabilities are the probabilities of each individual event or category. They can be computed by summing up the probabilities in either the row or column of a two-way table.

Question 18

The type of diagram that shows subsets of the population on different branches is called a:

Accepted Answer

A tree diagram displays a hierarchical structure, where each level represents a set of information, and each branch represents possible permutations or combinations of the sets. It is commonly used in probability and decision analysis. In contrast, a departmental diagram shows the organizational structure of a company, a Venn diagram shows the overlap between sets of objects or concepts, and a scattered diagram plots the relationship between two numerical variables.

Question 19

To determine the effectiveness of a new advertisement which is shown to one customer group and not another,followed by observation of the purchase behavior of both groups is determined by the use of:

Accepted Answer

The answer of To determine the effectiveness of a new...

Question 20

Permutations are employed in cases where the order of objects is not important.

Accepted Answer

Permutations are used when the order of objects is important. If the order of objects is not important, then combinations are used.

Quiz 3: Probability