Question 1

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 2

Which of the following is a requirement of the probabilities assigned to outcome O_i ? A)P ( O_i )£ 0 for each i B)P ( O_i )³ 1 for each i C)0 £ P ( O_i )£ 1 for each i D)P ( O_i )= 1 for each i

Accepted Answer

The requirement for any probability is that it must be between 0 and 1 (inclusive). Therefore, choice C is the correct answer.

Question 3

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 of an experiment. Choice C is a single outcome, whereas A and B are compound events (consisting of multiple outcomes) and D is not even an outcome in the sample space.

Question 4

Prior probability is also called likelihood probability.

Accepted Answer

Prior probability and likelihood probability are different concepts. Prior probability refers to the probability of an event occurring based on previous knowledge or information, whereas likelihood probability refers to the probability of obtaining a certain outcome given a specific set of conditions.

Question 5

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 assumes that all outcomes of the experiment are equally likely. Therefore, this approach assigns equal probabilities to each outcome.

Question 6

If joint, marginal, and conditional probabilities are available, only joint probabilities can be used to determine whether two events are dependent or independent.

Accepted Answer

Marginal and conditional probabilities, along with joint probabilities, can be used to determine whether two events are dependent or independent. If the joint probability of two events equals the product of their marginal probabilities, or if the conditional probability of one event given the other is the same as the marginal probability of the event, the events are independent.

Question 7

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

A sample space is the collection of all possible outcomes of an experiment.

Question 8

In general, a posterior probability is calculated by adding the prior and likelihood probabilities.

Accepted Answer

A posterior probability is calculated using Bayes' theorem, which involves multiplying the prior probability and likelihood probability, and then normalizing by the evidence (sum of all possible outcomes).

Question 9

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

A balanced die has six faces, with three of them being even (2, 4, 6) and three being odd (1, 3, 5), giving an even number a 50% chance of appearing on any given roll. Therefore, over 50 rolls, you would expect an even number to appear about 25 times on average.

Question 10

Suppose we have two events A and B . We can apply the addition rule to compute the probability that at least one of these events occurs.

Accepted Answer

The addition rule states that the probability of A or B occurring is equal to the probability of A plus the probability of B minus the probability that both A and B occur. Therefore, we can apply the addition rule to compute the probability that at least one of these events occurs.

Question 11

Posterior probabilities can be calculated using the addition rule for mutually exclusive events.

Accepted Answer

The addition rule for mutually exclusive events states that the probability of either event A or event B occurring is equal to the sum of their individual probabilities, P(A or B) = P(A) + P(B). However, calculating posterior probabilities usually involves events that are not mutually exclusive, so the addition rule cannot be used. The correct method for calculating posterior probabilities is through Bayes' Theorem.

Question 12

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 P(A) and P(B) cannot exceed 1. Given P(A) = 0.75, P(B) cannot be larger than 0.25 to ensure the total probability does not exceed 1.

Question 13

In problems where the joint probabilities are given, we can compute marginal probabilities by adding across rows and down columns.

Accepted Answer

Marginal probabilities can indeed be computed by adding across rows and down columns of the joint probability table.

Question 14

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 15

If an experiment consists of five outcomes with P ( O ₁)= 0.10, P ( O ₂)= 0.20, P ( O ₃)= 0.30, P ( O ₄)= 0.25, then P ( O ₅)is A)0.75 B)0.15 C)0.50 D)Cannot be determined from the information given.

Accepted Answer

The sum of probabilities for all outcomes in an experiment must equal 1. Adding the given probabilities: 0.10 + 0.20 + 0.30 + 0.25 = 0.85. Therefore, P(O₅) = 1 - 0.85 = 0.15.

Question 16

If two events are collectively exhaustive, what is the probability that both occur at the same time?
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 17

We can apply the multiplication rule to compute the probability that two events occur at the same time.

Accepted Answer

The multiplication rule states that the probability of two events occurring at the same time is equal to the product of their individual probabilities, assuming that the events are independent. Therefore, this statement is true.

Question 18

Prior probabilities can be calculated using the multiplication rule for mutually exclusive events.

Accepted Answer

The multiplication rule can only be used for independent events, not mutually exclusive events.

Question 19

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 calculating the fraction or proportion of times an event occurs in a sample. In this case, of the last 500 customers, 50 purchased a wireless phone, so the proportion or relative frequency is:

50/500 = 0.1 or 10%

Therefore, the probability that the next customer will purchase a wireless phone is 0.10 or 10%.

Question 20

We can use the joint and marginal probabilities to compute conditional probabilities, for which a formula is available.

Accepted Answer

This is true. We can use the formula for conditional probability, P(A|B) = P(A and B) / P(B), where P(A|B) is the probability of A given that B has occurred, P(A and B) is the joint probability of A and B occurring, and P(B) is the marginal probability of B occurring.

Quiz 5: Probability

Which of the following is an approach to assigning probabilities?

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

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?

Prior probability is also called likelihood probability.

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

If joint, marginal, and conditional probabilities are available, only joint probabilities can be used to determine whether two events are dependent or independent.

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

In general, a posterior probability is calculated by adding the prior and likelihood probabilities.

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

Suppose we have two events A and B . We can apply the addition rule to compute the probability that at least one of these events occurs.

Posterior probabilities can be calculated using the addition rule for mutually exclusive events.

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

In problems where the joint probabilities are given, we can compute marginal probabilities by adding across rows and down columns.

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

If an experiment consists of five outcomes with P ( O ₁) = 0.10, P ( O ₂) = 0.20, P ( O ₃) = 0.30, P ( O ₄) = 0.25, then P ( O ₅) is

If two events are collectively exhaustive, what is the probability that both occur at the same time?

We can apply the multiplication rule to compute the probability that two events occur at the same time.

Prior probabilities can be calculated using the multiplication rule for mutually exclusive events.

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

We can use the joint and marginal probabilities to compute conditional probabilities, for which a formula is available.

Quiz 5: Probability

Which of the following is an approach to assigning probabilities?

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

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?

Prior probability is also called likelihood probability.

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

If joint, marginal, and conditional probabilities are available, only joint probabilities can be used to determine whether two events are dependent or independent.

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

In general, a posterior probability is calculated by adding the prior and likelihood probabilities.

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

Suppose we have two events A and B . We can apply the addition rule to compute the probability that at least one of these events occurs.

Posterior probabilities can be calculated using the addition rule for mutually exclusive events.

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

In problems where the joint probabilities are given, we can compute marginal probabilities by adding across rows and down columns.

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

If an experiment consists of five outcomes with P ( O 1) = 0.10, P ( O 2) = 0.20, P ( O 3) = 0.30, P ( O 4) = 0.25, then P ( O 5) is

If two events are collectively exhaustive, what is the probability that both occur at the same time?

We can apply the multiplication rule to compute the probability that two events occur at the same time.

Prior probabilities can be calculated using the multiplication rule for mutually exclusive events.

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

We can use the joint and marginal probabilities to compute conditional probabilities, for which a formula is available.

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

If an experiment consists of five outcomes with P ( O ₁) = 0.10, P ( O ₂) = 0.20, P ( O ₃) = 0.30, P ( O ₄) = 0.25, then P ( O ₅) is