Question 1

An approach of assigning probabilities which assumes that all outcomes of the experiment are equally likely is referred to as the:
A) subjective approach
B) objective approach
C) classical approach
D) relative frequency approach

Accepted Answer

The classical approach, also known as the a priori approach, assumes that each possible outcome of an experiment is equally likely and assigns probabilities based on this assumption. This approach is used for simple random events where all possible outcomes are equally likely to occur. The subjective approach involves assigning probabilities based on personal judgments or beliefs, while the objective approach relies on observed data from past events. The relative frequency approach involves gathering data on past events to determine the likelihood of future outcomes.

Question 2

If A and B are mutually exclusive events with P(A) = 0.75, then P(B):
A) can be any value between 0 and 1.
B) can be any value between 0 and 0.75.
C) cannot be larger than 0.25.
D) equals 0.25.

Accepted Answer

Since A and B are mutually exclusive, they cannot both happen at the same time, meaning the sum of their probabilities cannot exceed 1. Given P(A) = 0.75, the maximum P(B) can be is 1 - 0.75 = 0.25, so it cannot be larger than 0.25.

Question 3

P(A) + P(B) = 1 for any events A and B that are mutually exclusive.

Accepted Answer

P(A) + P(B) = 1 only if A and B are complementary events, meaning one happens if the other does not. For mutually exclusive events, this equation does not necessarily hold unless they also cover the entire sample space.

Question 4

Of the last 500 customers entering a supermarket, 50 have purchased a wireless phone.If the relative frequency approach for assigning probabilities is used, the probability that the next customer will purchase a wireless phone is
A) 0.10
B) 0.90
C) 0.50
D) None of these choices.

Accepted Answer

The relative frequency approach for assigning probabilities involves using the frequency of past events to estimate the probability of future events.

In this case, out of the last 500 customers, 50 have purchased a wireless phone.

Therefore, the relative frequency of customers purchasing a wireless phone is 50/500 = 0.1 or 10%.

Using this approach, we can estimate the probability that the next customer will purchase a wireless phone to be 0.1 or 10%.

So, the best choice is A) 0.10.

Question 5

If events A and B cannot occur at the same time, they are called mutually exclusive.

Accepted Answer

This is the definition of mutually exclusive events. If events A and B cannot occur at the same time, they are said to be mutually exclusive.

Question 6

You think you have a 90% chance of passing your next advanced financial accounting exam.This is an example of subjective approach to probability.

Accepted Answer

This statement is based on the person's personal belief or judgment, rather than an objective calculation or measurement of probabilities. Therefore, it is an example of subjective approach to probability.

Question 7

Predicting the outcome of a football game is using the subjective approach to probability.

Accepted Answer

The subjective approach to probability involves using personal knowledge and experience to make predictions, which is exactly what is being done when predicting the outcome of a football game.

Question 8

If an experiment consists of five outcomes with P(O₁) = 0.10, P(O₂) = 0.20, P(O₃) = 0.30, P(O₄) = 0.25, then P(O₅) is A) 0.75 B) 0.15 C) 0.50 D) Cannot be determined from the information given.

Accepted Answer

The sum of the probabilities of all possible outcomes must equal 1. The sum of the probabilities given is 0.85 (0.10 + 0.20 + 0.30 + 0.25). Therefore, the probability of the fifth outcome can be found by subtracting the sum from 1: 1 - 0.85 = 0.15. Therefore, the probability of P(O₅) is 0.15.

Question 9

If P(A) = 0.4 and P(B) = 0.6, then A and B must be collectively exhaustive.

Accepted Answer

The probabilities of events A and B being 0.4 and 0.6, respectively, do not imply that A and B are collectively exhaustive. They could be independent, overlapping, or mutually exclusive events, and being collectively exhaustive depends on whether together they cover all possible outcomes, not just on their individual probabilities.

Question 10

If you roll a balanced die 50 times, you should expect an even number to appear:
A) on every other roll.
B) exactly 50 times out of 100 rolls.
C) 25 times on average, over the long term.
D) All of these choices are true.

Accepted Answer

The probability of rolling an even number on any one roll of a balanced die is 1/2. Therefore, we can expect an even number to appear on approximately 25 out of 50 rolls on average, over the long term. However, there is no guarantee that an even number will appear exactly 25 times, as the results of individual rolls are subject to chance. Choice A is not true because there may be stretches where multiple even numbers appear in a row, or multiple odd numbers appear. Choice B is not true because it implies a guarantee, when in fact the results are subject to chance.

Question 11

If either event A or event B must occur, then A and B are mutually exclusive and collectively exhaustive events.

Accepted Answer

The answer of If either event A or event B...

Question 12

A sample space of an experiment consists of the following outcomes: 1, 2, 3, 4, and 5.Which of the following is a simple event?
A) At least 3
B) At most 2
C) 3
D) 15

Accepted Answer

A simple event is a single outcome from a sample space. Option C, which is 3, is a single outcome and therefore a simple event. Options A and B are not simple events because they involve a range of outcomes rather than a single outcome. Option D is not a possible outcome in the given sample space.

Question 13

If two events are collectively exhaustive, what is the probability that one or the other occurs?
A) 0.00
B) 0.50
C) 1.00
D) Cannot be determined from the information given.

Accepted Answer

The answer of If two events are collectively exhaustive, what...

Question 14

Which of the following is a requirement of the probabilities assigned to outcome O_i? A) P(O_i)$\le$ 0 for each i B) P(O_i) $\ge$1 for each i C) 0$\le$P(O_i) $\le$ 1 for each i D) P(O_i) = 1 for each i

Accepted Answer

The probability assigned to outcome O_i must be between 0 and 1 for each i. Therefore, option C is the correct requirement. Options A and B have the wrong inequality signs, and option D states that the probability must be exactly 1, which could be incorrect as it depends on the specific situation.

Question 15

The collection of all the possible outcomes of a random experiment is called a sample space.

Accepted Answer

This is the definition of a sample space in probability theory.

Question 16

Which of the following is an approach to assigning probabilities?
A) Classical approach
B) Relative frequency approach
C) Subjective approach
D) All of these choices are true.

Accepted Answer

The answer of Which of the following is an approach...

Question 17

The collection of all possible outcomes of an experiment is called:
A) a simple event
B) a sample space
C) a sample
D) a population

Accepted Answer

Sample space is the collection of all possible outcomes of an experiment. A simple event is a single outcome of an experiment, and a sample is a subset of the population. Therefore, options A, C, and D are not correct answers.

Question 18

The relative frequency approach to probability uses long term relative frequencies, often based on past data.

Accepted Answer

The statement is true. The relative frequency approach to probability is based on observing long-term relative frequencies of events in order to estimate the probability of those events occurring. This approach often relies on past data as a way to make predictions about future events.

Question 19

If either event A or event B must occur, they are called mutually exclusive.

Accepted Answer

If either event A or event B must occur, they are not mutually exclusive. Mutually exclusive events cannot occur at the same time.

Question 20

If P(A) = 0.4 and P(B) = 0.6, then A and B must be mutually exclusive.

Accepted Answer

If A and B are mutually exclusive, then P(A ∩ B) = 0. However, we are not given information about their intersection, so we cannot conclude that they are mutually exclusive just based on their individual probabilities. Therefore, the answer is B.

Quiz 6: Probability

An approach of assigning probabilities which assumes that all outcomes of the experiment are equally likely is referred to as the:

If A and B are mutually exclusive events with P(A) = 0.75, then P(B) :

P(A) + P(B) = 1 for any events A and B that are mutually exclusive.

Of the last 500 customers entering a supermarket, 50 have purchased a wireless phone.If the relative frequency approach for assigning probabilities is used, the probability that the next customer will purchase a wireless phone is

If events A and B cannot occur at the same time, they are called mutually exclusive.

You think you have a 90% chance of passing your next advanced financial accounting exam.This is an example of subjective approach to probability.

Predicting the outcome of a football game is using the subjective approach to probability.

If an experiment consists of five outcomes with P(O₁) = 0.10, P(O₂) = 0.20, P(O₃) = 0.30, P(O₄) = 0.25, then P(O₅) is

If P(A) = 0.4 and P(B) = 0.6, then A and B must be collectively exhaustive.

If you roll a balanced die 50 times, you should expect an even number to appear:

If either event A or event B must occur, then A and B are mutually exclusive and collectively exhaustive events.

A sample space of an experiment consists of the following outcomes: 1, 2, 3, 4, and 5.Which of the following is a simple event?

If two events are collectively exhaustive, what is the probability that one or the other occurs?

Which of the following is a requirement of the probabilities assigned to outcome O_i?

The collection of all the possible outcomes of a random experiment is called a sample space.

Which of the following is an approach to assigning probabilities?

The collection of all possible outcomes of an experiment is called:

The relative frequency approach to probability uses long term relative frequencies, often based on past data.

If either event A or event B must occur, they are called mutually exclusive.

If P(A) = 0.4 and P(B) = 0.6, then A and B must be mutually exclusive.

Quiz 6: Probability

An approach of assigning probabilities which assumes that all outcomes of the experiment are equally likely is referred to as the:

If A and B are mutually exclusive events with P(A) = 0.75, then P(B) :

P(A) + P(B) = 1 for any events A and B that are mutually exclusive.

Of the last 500 customers entering a supermarket, 50 have purchased a wireless phone.If the relative frequency approach for assigning probabilities is used, the probability that the next customer will purchase a wireless phone is

If events A and B cannot occur at the same time, they are called mutually exclusive.

You think you have a 90% chance of passing your next advanced financial accounting exam.This is an example of subjective approach to probability.

Predicting the outcome of a football game is using the subjective approach to probability.

If an experiment consists of five outcomes with P(O1) = 0.10, P(O2) = 0.20, P(O3) = 0.30, P(O4) = 0.25, then P(O5) is

If P(A) = 0.4 and P(B) = 0.6, then A and B must be collectively exhaustive.

If you roll a balanced die 50 times, you should expect an even number to appear:

If either event A or event B must occur, then A and B are mutually exclusive and collectively exhaustive events.

A sample space of an experiment consists of the following outcomes: 1, 2, 3, 4, and 5.Which of the following is a simple event?

If two events are collectively exhaustive, what is the probability that one or the other occurs?

Which of the following is a requirement of the probabilities assigned to outcome Oi?

The collection of all the possible outcomes of a random experiment is called a sample space.

Which of the following is an approach to assigning probabilities?

The collection of all possible outcomes of an experiment is called:

The relative frequency approach to probability uses long term relative frequencies, often based on past data.

If either event A or event B must occur, they are called mutually exclusive.

If P(A) = 0.4 and P(B) = 0.6, then A and B must be mutually exclusive.

If an experiment consists of five outcomes with P(O₁) = 0.10, P(O₂) = 0.20, P(O₃) = 0.30, P(O₄) = 0.25, then P(O₅) is

Which of the following is a requirement of the probabilities assigned to outcome O_i?