Question 1

If events A and B are independent, then P(A) = P(A|B).

Accepted Answer

If events A and B are independent, the probability of A occurring does not change based on whether B occurs or not, hence P(A) = P(A|B).

Question 2

Two events A and B are said to be mutually exclusive if the occurrence of one event means that the other event cannot or will not occur; that is P(A $\cap$ B) = 0.

Accepted Answer

Mutually exclusive events mean that if one event occurs, the other cannot, which is mathematically represented as P(A ∩ B) = 0, indicating the probability of both events happening together is zero.

Question 3

When the results of experimentation or historical data are used to assign probability values, the method used to assign probabilities is referred to as the subjective method.

Accepted Answer

The method used to assign probabilities based on experimentation or historical data is referred to as the empirical or relative frequency method, not the subjective method. The subjective method involves using judgment, intuition, or expertise to assign probabilities.

Question 4

In a multi-stage experiment, if there are two outcomes per stage and there are three stages, then the total number of outcomes is six.

Accepted Answer

In a multi-stage experiment with two outcomes per stage and three stages, the total number of outcomes is calculated as 2^3 = 8, since each stage doubles the possible outcomes from the previous stage.

Question 5

Drew is a long-time employee at your coffee shop.Which would be the most appropriate method for estimating the probability that Drew will be on time to work next Monday morning?
A)the classical approach
B)the relative frequency approach
C)the subjective approach
D)the experimental method
E)none of the above

Accepted Answer

The relative frequency approach is most appropriate for estimating the probability that Drew will be on time, as it involves using past data (Drew's previous attendance records) to calculate the likelihood of an event occurring.

Question 6

In constructing a probability tree, probabilities beyond the first stage are conditional probabilities and the multiplication rule is used to get end node probabilities.

Accepted Answer

In a probability tree, probabilities beyond the first stage are indeed conditional probabilities, reflecting the probability of an event given the occurrence of a previous event. The multiplication rule is used to calculate the probability of a sequence of events by multiplying the probabilities along the branches leading to an end node.

Question 7

When the results of experimentation or historical data are used to assign probability values, the method used to assign probabilities is referred to as the:
A)relative frequency method
B)subjective method
C)classical method
D)posterior method
E)none of the above

Accepted Answer

The relative frequency method assigns probabilities based on the frequency of occurrence of an event in past data or experiments.

Question 8

Probability is a number between 0 and 1 that measures the chance or likelihood that some event or set of events will occur.

Accepted Answer

Probability quantifies the likelihood of an event happening, where 0 indicates impossibility and 1 indicates certainty.

Question 9

For the cases listed below, in which one would you most likely use the classical approach to assign probability?
A)the probability that at least one of the ten orders you placed on Amazon will be delivered late.
B)the probability that you will become famous.
C)the probability that you roll a five on one roll of two dice.
D)the probability that you it will snow be cloudy tomorrow.
E)the probability that you will pass the exam today.

Accepted Answer

The classical approach to probability is used when all outcomes are equally likely, such as rolling dice. Rolling a five on one roll of two dice involves a finite number of equally likely outcomes, making it suitable for the classical approach.

Question 10

A probability near 1 for an event indicates that the event is very unlikely to occur.

Accepted Answer

A probability near 1 indicates that the event is very likely to occur, not unlikely.

Question 11

A graphical method of representing the sample points or outcomes of a multiple step experiment is a Venn diagram.

Accepted Answer

A graphical method of representing the sample points or outcomes of a multiple step experiment is a tree diagram, not a Venn diagram. Venn diagrams are used to show all possible logical relations between a finite collection of different sets.

Question 12

Which of the following is NOT one of the basic requirements of probability? A)for each experimental outcome E_i, then 0 < P(E_i) < 1 for all i B)P(A) = P(A^') - 1 C)if there are k experimental outcomes, then P(E₁) + P(E₂) + … + P(E_k) = 1 D)both b and c E)all of the above

Accepted Answer

The correct basic requirements of probability include that the probability of any event is between 0 and 1, and the sum of probabilities of all possible outcomes must equal 1. Option B, which suggests a probability formula that results in a value of -1, does not align with these principles, making it incorrect.

Question 13

If events A and B are mutually exclusive, then P(A or B) = P(A)+P(B).

Accepted Answer

Mutually exclusive events cannot happen at the same time, so the probability of either event A or event B occurring is the sum of their individual probabilities.

Question 14

One of the basic requirements of probability is: A)for each experimental outcome E_i, we must have P(E_i) $\ge$ 1 B)P(A) = P(A^') - 1 C)if there are k experimental outcomes, then P(E₁) + P(E₂) + … + P(E_k) = 1 D)both b and c E)all of the above

Accepted Answer

The correct answer is C because it states that the sum of the probabilities of all possible experimental outcomes must equal 1, which is a fundamental requirement of probability.

Question 15

Two events are mutually exclusive if the probability of their intersection is 0.5.

Accepted Answer

Two events are mutually exclusive if they cannot both occur at the same time, which means the probability of their intersection is 0, not 0.5.

Question 16

For the cases listed below, in which one would you most likely use the subjective approach to assign probability?
A)the probability of being chosen randomly from your class of 30 students to lead today's class discussion.
B)the probability that your friend Kyle will pick up the check for lunch.
C)the probability that you will guess the right answer on a multiple choice test question.
D)the probability that you produce at least ten heads when you flip a quarter 20 times.
E)the probability that you will an ace of spades from a 52-card deck of cards.

Accepted Answer

The subjective approach to assigning probability is used when the probability is based on personal judgment rather than on an objective calculation or physical measurement. In the case of predicting whether your friend Kyle will pick up the check for lunch, this decision would likely be based on personal judgment about Kyle's past behavior, personality, or current situation, making it a subjective probability.

Question 17

A probability near 0 for an event indicates that the event is very likely to occur.

Accepted Answer

A probability near 0 indicates that the event is very unlikely to occur.

Question 18

Each individual outcome of an experiment is called a sample point.

Accepted Answer

A sample point represents an individual outcome of an experiment in probability theory, which is the most basic outcome that cannot be broken down further.

Question 19

Probability is defined as the numerical measure of the likelihood that an event will occur and is always between 0 and 1.

Accepted Answer

Probability values range from 0 to 1, where 0 indicates an impossibility of the event occurring, and 1 indicates certainty.

Question 20

If events A and B are independent, then P(A and b) = P(A)*P(B).

Accepted Answer

If events A and B are independent, the probability of both A and B occurring (P(A and B)) is indeed the product of their individual probabilities, P(A) * P(B).

Quiz 4: Probability

If events A and B are independent, then P(A) = P(A|B).

Two events A and B are said to be mutually exclusive if the occurrence of one event means that the other event cannot or will not occur; that is P(A ∩\cap∩ B) = 0.

When the results of experimentation or historical data are used to assign probability values, the method used to assign probabilities is referred to as the subjective method.

In a multi-stage experiment, if there are two outcomes per stage and there are three stages, then the total number of outcomes is six.

Drew is a long-time employee at your coffee shop.Which would be the most appropriate method for estimating the probability that Drew will be on time to work next Monday morning?

In constructing a probability tree, probabilities beyond the first stage are conditional probabilities and the multiplication rule is used to get end node probabilities.

When the results of experimentation or historical data are used to assign probability values, the method used to assign probabilities is referred to as the: