Master Probability Fundamentals: Interactive Quizzes for Statistics MSc

Question 1

Which of the following is NOT an application of probability theory?

Accepted Answer

Explaining the behavior of subatomic particles

Answer

Risk assessment in finance

Answer

Statistical inference in scientific research

Answer

Predicting weather patterns

Question 2

Which axiom of probability states that no event's probability can be below 0 or above 1?

Accepted Answer

The non-negativity axiom

Answer

The additivity axiom

Answer

The complement axiom

Answer

The conditional probability axiom

Question 3

Which of the following is a fundamental axiom of probability?

Accepted Answer

The probability of the sample space is always equal to 1.

Answer

The probability of an event being negative is valid.

Answer

The probability of an event is less than or equal to 0.

Answer

The probability of the union of two events is consistently less than the probability of each event.

Question 4

When rolling a fair six-sided die twice, what's the probability of getting a total of 7?

Accepted Answer

1/12

Answer

1/6

Answer

1/18

Answer

1/24

Question 5

In probability theory, define 'independent events' and explain their significance.

Accepted Answer

Independent events are events whose probabilities remain unaffected by the occurrence or non-occurrence of other events.

Answer

Independent events are events that always occur together.

Answer

Independent events are events that are mutually exclusive.

Question 6

Which of the following is NOT an axiom of probability theory?

Accepted Answer

The probability of the event that the outcome of an experiment is a number between 0 and 1 is 1.

Answer

The probability of an event cannot be negative.

Answer

The probability of an event occurring is between 0 and 1, inclusive.

Answer

The sum of the probabilities of all possible outcomes of an experiment equals 1.

Question 7

A sample space is:

Accepted Answer

The set of all possible outcomes of an experiment.

Answer

The set of outcomes of an event in an experiment.

Answer

The set of all possible values of a random variable.

Answer

The set of probabilistic events in an experiment.

Question 8

Which of the following statements about the probability of the union of two events is true?

Accepted Answer

It can be greater than, less than, or equal to the sum of the probabilities of the two events.

Answer

It is always greater than the probability of either event.

Answer

It is always less than the probability of either event.

Answer

It is always equal to the sum of the probabilities of the two events.

Question 9

A sample space is defined as the:

Accepted Answer

Set of all possible outcomes of an experiment or study.

Answer

Event with the highest probability of occurring.

Answer

Complement of the impossible event.

Answer

Intersection of all events in the experiment.

Question 10

Which of the following is an example of a continuous random variable?

Accepted Answer

Height of a randomly selected person.

Answer

Number of heads in 10 coin flips.

Answer

Number of siblings in a family.

Answer

Age of a randomly selected car.

Question 11

What is the probability of getting at least one head when flipping three coins?

Accepted Answer

0.75

Answer

0.25

Answer

0.5

Answer

1

Question 12

The central limit theorem states that:

Accepted Answer

The distribution of sample means approaches a normal distribution as the sample size increases.

Answer

The probability of getting a head on a coin flip is always 50%.

Answer

The expected value of a random variable is always equal to its variance.

Answer

The median of a random variable is always greater than its mean.

Question 13

Two events, A and B, are independent if:

Accepted Answer

P(A|B) = P(A)

Answer

P(A|B) = 0

Answer

P(A) + P(B) = P(A ∩ B)

Answer

P(A|B) = 1

Question 14

Which of the following is an example of a continuous random variable?

Accepted Answer

The height of a randomly selected adult male

Answer

The number of siblings a person has

Answer

The number of heads obtained when flipping a coin 10 times

Answer

The number of customers in a store on a given day

Question 15

The expected value of a random variable X represents its:

Accepted Answer

Average value over all possible outcomes

Answer

Most likely outcome

Answer

Standard deviation

Answer

Range of possible values

Question 16

Which of the following is NOT a measure of variability for a dataset?

Accepted Answer

Mean

Answer

Variance

Answer

Standard deviation

Answer

Interquartile range

Question 17

Which of the following is a fundamental axiom of probability?

Accepted Answer

The probability of an event is a number between 0 and 1, inclusive.

Answer

The probability of an event can be negative.

Answer

The probability of the complement of an event is always greater than the probability of the event.

Answer

The probability of the union of two independent events is the product of their probabilities.

Question 18

A bag contains five red marbles, three blue marbles, and two green marbles. What is the probability of drawing a red marble?

Accepted Answer

5/10 or 1/2

Answer

1/10

Answer

3/10

Answer

2/10

Question 19

Which of the following is an example of a conditional probability?

Accepted Answer

The probability of an event A occurring given that event B has already occurred.

Answer

The probability of event B occurring.

Answer

The probability of event A occurring.

Question 20

What is the complement of the event "rolling an even number on a standard six-sided die"?

Accepted Answer

Rolling an odd number on a standard six-sided die

Answer

Rolling a number greater than 3 on a standard six-sided die

Answer

Rolling a multiple of 5 on a standard six-sided die

Question 21

What is the probability of drawing a face card (Jack, Queen, or King) from a standard deck of 52 cards?

Accepted Answer

12/52 or 3/13

Answer

26/52

Answer

1/2

Answer

1/4

Question 22

What is the probability of getting exactly two heads when a fair coin is tossed four times?

Accepted Answer

6/16 or 3/8

Answer

1/16

Answer

3/4

Answer

1/2

Question 23

Which of the following is a key assumption of probability theory?

Accepted Answer

The outcomes of an experiment are random and unpredictable.

Answer

The probability of an event can be determined with certainty.

Answer

The sample space is always infinite.

Question 24

In the context of probability theory, the fundamental unit of analysis is known as the

Accepted Answer

Sample space

Answer

Conditional probability

Answer

Event

Answer

Probability axiom

Question 25

In probability theory, a set of outcomes is termed a

Accepted Answer

Event

Answer

Sample space

Answer

Distribution

Answer

Random variable

Question 26

Given events A and B, the conditional probability of event A occurring if event B has already occurred is denoted as

Accepted Answer

P(A|B) = P(A ∩ B) / P(B)

Answer

P(A|B) = P(A) / P(B)

Answer

P(A|B) = P(B) / P(A)

Answer

P(A|B) = P(A ∩ B)

Question 27

The complement of an event is defined as the set of all outcomes that are

Accepted Answer

not in the event

Answer

independent of the event

Answer

in the event

Answer

mutually exclusive with the event

Question 28

The expected value of a random variable is a measure of its

Accepted Answer

central tendency

Answer

spread

Answer

kurtosis

Answer

skewness

Question 29

The standard deviation of a random variable is a measure of its

Accepted Answer

dispersion

Answer

skewness

Answer

kurtosis

Answer

central tendency

Question 30

A bag contains 5 red balls and 3 blue balls. Two balls are selected randomly without replacement. What is the probability that both balls are red?

Accepted Answer

5/14

Answer

1/2

Answer

5/8

Answer

10/56

Question 31

Which of the following statements is NOT a property of probability?

Accepted Answer

The probability of an event can be greater than 1.

Answer

The probability of the union of two mutually exclusive events is the sum of their individual probabilities.

Answer

The probability of an event is a number between 0 and 1.

Answer

The probability of the sample space is 1.

Question 32

A standard six-sided die is rolled. What is the probability of getting an even number or a number greater than 4?

Accepted Answer

2/3

Answer

1/3

Answer

5/6

Answer

1/2

Question 33

Two events A and B are considered independent if:

Accepted Answer

The probability of both A and B occurring is equal to the product of their individual probabilities: P(A and B) = P(A) * P(B)

Answer

The probability of A or B occurring is equal to the sum of their individual probabilities: P(A or B) = P(A) + P(B)

Answer

The probability of A given that B has occurred is equal to the probability of A: P(A|B) = P(A)

Answer

The probability of A is equal to the probability of B: P(A) = P(B)

Question 34

A random variable X is a variable whose value:

Accepted Answer

represents a numerical outcome of a random phenomenon.

Answer

can only take on discrete values.

Answer

is determined by a deterministic process.

Answer

is always constant.

Question 35

A box contains 10 red balls, 5 blue balls, and 5 green balls. If a ball is selected at random, what is the probability that it is either red or green?

Accepted Answer

3/4

Answer

1/2

Answer

1/4

Answer

2/3

Question 36

Which of the following is an example of a discrete random variable?

Accepted Answer

The number of heads in four coin tosses.

Answer

The height of a randomly selected student.

Answer

The time it takes to complete a task.

Answer

The temperature of a room.

Question 37

A fair coin is flipped twice. What is the probability of getting at least one head?

Accepted Answer

3/4

Answer

1/2

Answer

1/4

Answer

1/8

Question 38

A bag contains 3 red balls, 2 blue balls, and 1 green ball. If two balls are drawn randomly without replacement, what is the probability that both balls are the same color?

Accepted Answer

11/30

Answer

1/3

Answer

2/5

Answer

1/2