Question 1

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

D

Question 2

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

Accepted Answer

If A and B are mutually exclusive, this means that they cannot occur at the same time. Therefore, the probability of both A and B occurring together (P(AB)) is 0.

Question 3

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 revised probabilities of events based on additional information. They are calculated using Bayes' theorem and take into account prior probabilities, likelihoods, and new evidence to update the probabilities of events.

Question 4

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. A sample point is a single outcome of an experiment, but not the process itself. An event is a set of outcomes of an experiment. Therefore, the best choice is B, as it fits the given description.

Question 5

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 represents a single possible outcome of an experiment. An event is a collection of sample points, an estimator is a statistical tool used to estimate a population parameter, and an outlier is a data point that falls far outside the expected range of values.

Question 6

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 has 2 possible outcomes (heads or tails). Therefore, the total number of possible outcomes for tossing 4 coins is 2 x 2 x 2 x 2 = 16. Each toss is independent, so the sample space can be listed using a tree diagram or by listing all 16 possible outcomes: 
HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT.

Question 7

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 defined as the values between zero and one, where zero means an event is impossible and one means it is certain. Therefore, choice C is the best option as it accurately reflects the range of probability.

Question 8

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 9

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 is the set of all possible outcomes or sample points that can occur in a given experiment. This is a fundamental concept in probability theory, and is used to help calculate probabilities of events that may occur in the experiment. Choices A, B, and D are not correct as they do not accurately describe the sample space.

Question 10

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 11

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.

Question 12

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 possibilities at each step. Therefore, the total number of outcomes is 4 x 3 x 2 = 24. Therefore, choice C is the best answer.

Question 13

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

Accepted Answer

Posterior probabilities are conditional probabilities, which are calculated after taking into consideration new information or data. Therefore, the best choice is D - conditional probabilities. The other options listed (A,B,C) refer to different types of probabilities, but do not specifically refer to conditional probabilities.

Question 14

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 states that the probability of the intersection of two independent events is the product of their individual probabilities.

Question 15

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 single possible outcome of an experiment. It represents a specific result or observation that can occur, such as rolling a 3 on a dice or getting heads on a coin flip. Options A and B are incorrect because they refer to probability measures and the entire set of possible outcomes, respectively, rather than individual outcomes. Option D is technically true, but not as specific as option C.

Question 16

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

Accepted Answer

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

Question 17

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

Accepted Answer

A sample point is a single outcome of an experiment. The sample space is the set of all possible outcomes, not each individual outcome. "Experiment" and "individual" are too broad and do not specifically refer to an outcome of an experiment.

Question 18

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

Sample space refers to the set of all possible experimental outcomes. Therefore, option C is the correct choice. Options A, B, and D are incorrect because they do not reflect the entire set of possible outcomes.

Question 19

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

Accepted Answer

In statistical experiments, the outcome is not necessarily deterministic and can vary each time the experiment is repeated, which means that a different outcome may occur.

Question 20

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

The probability of getting at least one head in two flips of a coin can be found by calculating the probability of getting no heads (i.e. getting two tails) and subtracting that probability from 1. The probability of getting tails on the first flip is 1/2, and the probability of getting tails on the second flip is also 1/2. Therefore, the probability of getting two tails is (1/2) * (1/2) = 1/4. Subtracting this probability from 1 gives us the probability of getting at least one head: 1 - 1/4 = 3/4, or 0.75. So the best choice is C.

Quiz 4: Introduction to Probability

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

If A and B are mutually exclusive, then

Revised probabilities of events based on additional information are

Any process that generates well-defined outcomes 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 range of probability 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

The set of all possible sample points (experimental outcomes) 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

Posterior probabilities are computed using

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

Posterior probabilities are

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

A sample point refers to a(n)

The complement of P(A | B) is

Each individual outcome of an experiment is called

The sample space refers to

In statistical experiments, each time the experiment is repeated

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