Master Probability Basics: Interactive Quizzes for Business Statistics

Question 1

A standard deck of cards contains 52 cards. What is the probability of drawing an ace from a well-shuffled deck?

Accepted Answer

1/13

Answer

4/13

Answer

1/4

Answer

1/2

Question 2

Two events, A and B, are independent if:

Accepted Answer

The occurrence of A does not affect the probability of B.

Answer

The occurrence of A increases the probability of B.

Answer

The occurrence of A decreases the probability of B.

Answer

The occurrence of A and B is equally likely.

Question 3

Which of the following probability distributions is most appropriate for modeling the time between two events that occur randomly and independently of each other?

Accepted Answer

Exponential distribution

Answer

Poisson distribution

Answer

Binomial distribution

Answer

Normal distribution

Question 4

A manufacturing company produces three types of products: A, B, and C. Which of the following represents the sample space for the type of product produced?

Accepted Answer

{A, B, C}

Answer

{A, B, C, D}

Answer

{P, Q, R}

Answer

{1, 2, 3}

Question 5

Which probability axiom defines the range of possible probability values, ensuring they are always non-negative?

Accepted Answer

Axiom of Non-Negativity

Answer

Axiom of Additivity

Answer

Axiom of Complement

Answer

Axiom of Conditional Probability

Question 6

Which of the following options does NOT adhere to the fundamental probability axioms?

Accepted Answer

An event's probability is always less than its complement's probability.

Answer

Probability values range between 0 and 1.

Answer

The probability of an impossible event is 0.

Answer

The probability of the sample space is always 1.

Question 7

What accurately describes the sample space of an experiment?

Accepted Answer

The collection of all conceivable outcomes.

Answer

A subset of all possible outcomes.

Answer

A potentially empty set.

Answer

A set with a finite number of elements.

Question 8

When tossing a fair coin twice, what is the probability of obtaining tails on the first toss and heads on the second?

Accepted Answer

1/4

Answer

1/2

Answer

1

Answer

1/8

Question 9

Which of these is NOT a property of conditional probability?

Accepted Answer

Can be greater than the probability of the conditioning event.

Answer

Can be defined for any two events.

Answer

Always a value between 0 and 1.

Answer

Calculated by dividing the joint probability by the conditioning event's probability.

Question 10

In a bag with 5 red marbles and 4 blue marbles, if two marbles are drawn sequentially without replacement, what is the probability of drawing two blue marbles?

Accepted Answer

4/45

Answer

1/9

Answer

1/6

Answer

2/9

Question 11

What is the defining characteristic of mutually exclusive events?

Accepted Answer

They cannot occur simultaneously.

Answer

They can occur simultaneously.

Answer

Their probabilities are always equal.

Answer

Their probabilities always sum to 1.

Question 12

In a sample space, what is an event?

Accepted Answer

A subset of the sample space

Answer

An element of the sample space

Answer

The entire sample space

Answer

The complement of the sample space

Question 13

Which fundamental rule of probability states that the probability of an event must be within which range?

Accepted Answer

Between 0 and 1, inclusive

Answer

Between -1 and 1, exclusive

Answer

Between 0 and 1, exclusive

Answer

Between -1 and 1, inclusive

Question 14

If event A has a probability of 0.3 and event B has a probability of 0.4, what is the probability of both events occurring (A and B)?

Accepted Answer

0.12

Answer

0.7

Answer

0.3

Answer

0.4

Question 15

Which scenario best exemplifies conditional probability?

Accepted Answer

The probability of getting hired for a job given that you have a certain certification

Answer

The probability of drawing a red card from a shuffled deck

Answer

The probability of rolling a 6 on a standard dice

Question 16

What's the distinction between a sample space and an event?

Accepted Answer

A sample space encompasses all possible outcomes, while an event represents a specific set of outcomes within that sample space

Answer

An event encompasses all possible outcomes, while a sample space represents a specific set of outcomes within that event

Answer

A sample space and an event are essentially the same concept

Question 17

Define the expected value of a random variable.

Accepted Answer

The average value of the random variable over all possible outcomes, weighted by their respective probabilities

Answer

The minimum possible value of the random variable

Answer

The maximum possible value of the random variable

Answer

The most frequently occurring value of the random variable

Question 18

Which statistical measure quantifies the spread or variability of a dataset?

Accepted Answer

Variance

Answer

Median

Answer

Mode

Answer

Mean

Question 19

What does the Law of Large Numbers imply?

Accepted Answer

As the sample size increases, the sample mean tends to converge towards the expected value of the underlying population

Answer

As the sample size increases, the probability of selecting any particular value approaches zero

Answer

As the sample size increases, the sample variance tends to decrease

Question 20

Which of the following is NOT an axiom of probability?

Accepted Answer

The probability of an event is strictly negative.

Answer

The probability of an event cannot exceed 1.

Answer

The probability of an empty event (the sample space) is always 1.

Answer

The sum of probabilities of a mutually exclusive event and its complement is 1.

Question 21

Two events, A and B, are independent if:

Accepted Answer

The occurrence of event A does not influence the probability of event B, and vice versa.

Answer

The events are mutually exclusive.

Answer

The events are equally likely to occur.

Question 22

What is the probability of an event not occurring?

Accepted Answer

1 minus the probability of the event occurring

Answer

Half of the event's probability

Answer

The inverse of the event's probability

Answer

The negative of the event's probability

Question 23

Two events, A and B, are mutually exclusive if:

Accepted Answer

They cannot both occur at the same time.

Answer

They are equally likely to occur.

Answer

The occurrence of one event increases the likelihood of the other occurring.

Answer

They have the same probability of occurrence.

Question 24

What is the probability of rolling an even number on a fair, six-sided die?

Accepted Answer

1/2

Answer

2/3

Answer

1/3

Answer

1/6

Question 25

Two events, A and B, are dependent if:

Accepted Answer

The occurrence of event A influences the probability of event B, and vice versa.

Answer

The events are equally likely to occur.

Answer

The events are mutually exclusive.

Question 26

In a standard deck of 52 cards, what is the probability of drawing a face card (jack, queen, or king)?

Accepted Answer

3/13

Answer

1/2

Answer

1/4

Answer

1/3

Question 27

What is the probability of an event that is guaranteed to occur?

Accepted Answer

1

Answer

-1

Answer

0

Answer

0.5

Question 28

In a deck of 52 cards, what is the probability of selecting a black card?

Accepted Answer

1/2

Answer

1/3

Answer

1/5

Answer

1/4

Question 29

What is the definition of conditional probability?

Accepted Answer

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

Answer

The probability of the intersection of two events.

Answer

The probability of the union of two events.

Question 30

Two fair dice are rolled. What is the probability of rolling a 6 on the first die and a 1 on the second die?

Accepted Answer

(1/6) * (1/6)

Answer

(1/6) + (1/6)

Answer

(1/6) / (1/6)

Answer

1 - (1/6) * (1/6)

Question 31

A bag contains 5 red balls and 7 blue balls. If three balls are drawn randomly, what is the probability that they are all red?

Accepted Answer

(5/12) * (4/11) * (3/10)

Answer

(5/12) + (4/11) + (3/10)

Answer

(5/12) / (4/11) + (3/10)

Answer

1 - (5/12) * (4/11) * (3/10)

Question 32

What type of probability distribution is used for a random variable that can take on any value within a specified range?

Accepted Answer

Normal distribution

Answer

Poisson distribution

Answer

Exponential distribution

Answer

Binomial distribution

Question 33

Which of the following is an axiom of probability?

Accepted Answer

The probability of an event is between 0 and 1.

Answer

The probability of an event can be greater than 1.

Answer

The probability of an event can be negative.

Question 34

A survey of 100 students found that 60% of them liked math and 40% of them liked science. If 20% of the students liked both math and science, what is the probability that a randomly selected student likes math or science?

Accepted Answer

0.8

Answer

0.6

Answer

0.4

Answer

0.2

Question 35

A fair coin is flipped. What is the probability of getting heads?

Accepted Answer

0.5

Answer

1

Answer

0.25

Answer

0.75

Question 36

Which of the following is NOT an axiom of probability?

Accepted Answer

The sum of the probabilities of all possible events in a sample space is less than 1.

Answer

The probability of an event is between 0 and 1.

Answer

If two events are mutually exclusive, their probabilities can be added.

Answer

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

Question 37

A company has a marketing campaign that has a 20% success rate. What is the probability that a randomly selected customer will respond to the campaign?

Accepted Answer

0.2

Answer

0.3

Answer

0.5

Question 38

A lot contains 10 items, of which 3 are defective. What is the probability of randomly selecting a non-defective item?

Accepted Answer

7/10

Answer

3/10

Answer

1/2

Question 39

Two events A and B are mutually exclusive. What is the probability of their intersection?

Accepted Answer

0

Answer

0.5

Answer

Cannot be determined

Answer

1

Question 40

A bag contains 4 red balls, 3 blue balls, and 2 green balls. What is the probability of drawing a red ball or a blue ball?

Accepted Answer

7/9

Answer

2/3

Answer

3/4

Answer

1/2

Question 41

Which of the following is NOT a fundamental probability axiom?

Accepted Answer

Probabilities must be greater than 1

Answer

The probability of an event is between 0 and 1

Answer

The sum of probabilities of all possible events is 1

Question 42

A fair coin is tossed. What is the sample space?

Accepted Answer

{Head, Tail}

Answer

{1, 2}

Answer

{Yes, No}

Answer

{True, False}

Question 43

An event has a probability of 0.25. What is the probability of the complement of this event?

Accepted Answer

0.75

Answer

0.35

Answer

0.50

Question 44

Two dice are rolled. What is the probability of rolling a sum of 7?

Accepted Answer

1 / 6

Answer

1 / 12

Answer

1 / 5

Question 45

A card is drawn from a standard deck of 52 cards. What is the probability of drawing a red face card?

Accepted Answer

1 / 4

Answer

1 / 26

Answer

1 / 13

Answer

1 / 6

Question 46

What is the probability of drawing a spade or a king from a standard deck of 52 cards?

Accepted Answer

23 / 52

Answer

13 / 26

Answer

1 / 4

Answer

13 / 52

Question 47

Two events A and B are independent. If P(A) = 0.6 and P(B) = 0.8, what is P(A ⋂ B)?

Accepted Answer

0.48

Answer

0.72

Answer

0.5

Answer

0.64

Question 48

What is the probability of getting a sum of 10 or 11 when rolling two fair dice?

Accepted Answer

1 / 6

Answer

1 / 3

Answer

1 / 4

Answer

1 / 5

Question 49

A bag contains 3 red marbles, 5 blue marbles, and 2 green marbles. If two marbles are drawn randomly and without replacement, what is the probability of drawing a red marble and then a green marble?

Accepted Answer

3 / 20

Answer

1 / 6

Answer

1 / 15

Answer

1 / 10

Question 50

A manufacturing process produces items with a 5% defect rate. What is the probability that a random sample of 10 items will include exactly 2 defective items?

Accepted Answer

0.1841

Answer

0.25

Answer

0.125

Answer

0.05