Question 1

In statistical experiments, each time the experiment is repeated
A)the same outcome must occur
B)the same outcome cannot occur again
C)a different outcome may occur
D)None of the other answers is correct.

Accepted Answer

In statistical experiments, each repetition of the experiment may result in a different outcome depending on the inherent randomness or variability in the data. Therefore, a different outcome may occur each time the experiment is repeated. The other options (A and B) are not true because in some experiments, there may be variability in the data and some outcomes may be more likely to occur than others. Option D is incorrect because there is a correct answer in this case (option C).

Question 2

Any process that generates well-defined outcomes is
A)an event
B)an experiment
C)a sample point
D)None of the other answers is correct.

Accepted Answer

An experiment is a process that generates well-defined outcomes, typically involving the manipulation of one or more independent variables to observe their effect on a dependent variable. Option A, "an event," is too broad and non-specific to fit the definition of a process that generates well-defined outcomes. Option C, "a sample point," is typically used in the context of probability theory to refer to a possible outcome of an experiment or event, and does not refer to the process itself. Option D, "None of the other answers is correct," is incorrect because option B is the correct answer.

Question 3

Three applications for admission to a local university are checked to determine whether each applicant is male or female. The number of sample points in this experiment is
A)2
B)4
C)6
D)8

Accepted Answer

Each applicant can be either male or female, so for each of the three applicants, there are 2 possibilities. Therefore, the total number of sample points is 2^3 = 8.

Question 4

An element of the sample space is
A)an event
B)an estimator
C)a sample point
D)an outlier

Accepted Answer

An element of the sample space is a sample point, which is a single outcome of an experiment.

Question 5

An experiment consists of tossing 4 coins successively. The number of sample points in this experiment is
A)16
B)8
C)4
D)2

Accepted Answer

Each coin can have 2 outcomes (heads or tails) and there are 4 coins, so the number of sample points is 2*2*2*2 = 16.

Question 6

The sample space refers to
A)any particular experimental outcome
B)the sample size minus one
C)the set of all possible experimental outcomes
D)both any particular experimental outcome and the set of all possible experimental outcomes are correct

Accepted Answer

The sample space refers to the set of all possible experimental outcomes. It is the collection of all possible outcomes that could occur in an experiment.

Question 7

If A and B are mutually exclusive, then
A)P(A) + P(B) = 0
B)P(A) + P(B) = 1
C)P(A I B) = 0
D)P(A I B) = 1

Accepted Answer

If two events A and B are mutually exclusive, then it means that they cannot happen at the same time. Therefore, the probability of their intersection (A ∩ B) will be 0. So, P(A ∩ B) = 0, which is equivalent to saying that P(A I B) = 0.

Question 8

The probability of at least one head in two flips of a coin is
A)0.33
B)0.50
C)0.75
D)1.00

Accepted Answer

To find the probability of at least one head in two flips of a coin, we need to find the probability of getting one head and the probability of getting two heads and then add them together. The probability of getting one head in one flip is 1/2, so the probability of getting one head in two flips is 1/2 + 1/2 - (1/2*1/2) = 3/4 = 0.75. Therefore, the best choice is C.

Question 9

The complement of P(A | B) is A)P(A^C | B) B)P(A | B^C) C)P(B | A) D)P(A I B)

Accepted Answer

The answer of The complement of P(A | B) is A)P(A^C...

Question 10

Revised probabilities of events based on additional information are
A)joint probabilities
B)posterior probabilities
C)marginal probabilities
D)complementary probabilities

Accepted Answer

Posterior probabilities are probabilities that have been updated based on new information, commonly by applying Bayes' theorem. Thus, revised probabilities of events based on additional information are posterior probabilities.

Question 11

The probability of an intersection of two events is computed using the
A)addition law
B)subtraction law
C)multiplication law
D)division law

Accepted Answer

The multiplication law is used to compute the probability of an intersection (also known as the joint probability) of two events. It states that for two independent events A and B, the probability of their intersection is equal to the probability of A multiplied by the probability of B, i.e. P(A and B) = P(A) * P(B). For dependent events, the formula takes into account the conditional probability of B given A, i.e. P(A and B) = P(A) * P(B|A).

Question 12

Posterior probabilities are computed using
A)the classical method
B)Chebyshev's theorem
C)the empirical rule
D)Bayes' theorem

Accepted Answer

Posterior probabilities are computed using Bayes' theorem, which involves updating prior probabilities based on new information or evidence. Chebyshev's theorem and the empirical rule are used to make generalizations about the spread of data in a distribution, while the classical method refers to using theoretical probabilities based on assumptions about the situation.

Question 13

A sample point refers to a(n)
A)numerical measure of the likelihood of the occurrence of an event
B)set of all possible experimental outcomes
C)individual outcome of an experiment
D)All of these answers are correct.

Accepted Answer

A sample point is a specific individual outcome of an experiment. It is not a numerical measure or the set of all possible outcomes.

Question 14

The range of probability is
A)any value larger than zero
B)any value between minus infinity to plus infinity
C)zero to one
D)any value between -1 to 1

Accepted Answer

The range of probability is always from 0 to 1 (inclusive), as the probability of an event can never be less than 0% or more than 100%.

Question 15

Since the sun must rise tomorrow, then the probability of the sun rising tomorrow is
A)much larger than one
B)zero
C)infinity
D)None of the other answers is correct.

Accepted Answer

Probabilities are always between 0 and 1, inclusive. The statement "the sun must rise tomorrow" implies certainty, which corresponds to a probability of 1, not larger than one, zero, or infinity.

Question 16

Posterior probabilities are
A)simple probabilities
B)marginal probabilities
C)joint probabilities
D)conditional probabilities

Accepted Answer

Posterior probabilities are conditional probabilities, which describe the probability of an event given that another event has occurred.

Question 17

An experiment consists of three steps. There are four possible results on the first step, three possible results on the second step, and two possible results on the third step. The total number of experimental outcomes is
A)9
B)14
C)24
D)36

Accepted Answer

The total number of experimental outcomes is found by multiplying the number of results at each step. 
4 × 3 × 2 = 24. Therefore, the best choice is C, which is 24.

Question 18

Each individual outcome of an experiment is called
A)the sample space
B)a sample point
C)an experiment
D)an individual

Accepted Answer

Each individual outcome of an experiment is typically referred to as a sample point.

Question 19

A lottery is conducted using three urns. Each urn contains chips numbered from 0 to 9. One chip is selected at random from each urn. The total number of sample points in the sample space is
A)30
B)100
C)729
D)1,000

Accepted Answer

The answer of A lottery is conducted using three urns....

Question 20

The set of all possible sample points (experimental outcomes) is called
A)a sample
B)an event
C)the sample space
D)a population

Accepted Answer

The sample space refers to the set of all possible outcomes or sample points in an experiment. The other options are not appropriate definitions for the sample space - a sample is a subset of the population, an event is a subset of the sample space, and a population refers to the entire group under study.

Quiz 4: Introduction to Probability

In statistical experiments, each time the experiment is repeated

Any process that generates well-defined outcomes is

Three applications for admission to a local university are checked to determine whether each applicant is male or female. The number of sample points in this experiment is

An element of the sample space is

An experiment consists of tossing 4 coins successively. The number of sample points in this experiment is

The sample space refers to

If A and B are mutually exclusive, then

The probability of at least one head in two flips of a coin is

The complement of P(A | B) is

Revised probabilities of events based on additional information are

The probability of an intersection of two events is computed using the

Posterior probabilities are computed using

A sample point refers to a(n)

The range of probability is

Since the sun must rise tomorrow, then the probability of the sun rising tomorrow is

Posterior probabilities are

An experiment consists of three steps. There are four possible results on the first step, three possible results on the second step, and two possible results on the third step. The total number of experimental outcomes is

Each individual outcome of an experiment is called

A lottery is conducted using three urns. Each urn contains chips numbered from 0 to 9. One chip is selected at random from each urn. The total number of sample points in the sample space is

The set of all possible sample points (experimental outcomes) is called