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Probability & Combinatorics Quiz

Total questions: 61

Worksheet time: 31mins

Name
Class
Date
1.

If an event always occurs in every trial, it is called:

a)

Impossible event

b)

Random event

c)

Certain event

d)

Dependent event

e)

Complementary event

2.

Who first gave the classical definition of probability?

a)

Pascal

b)

Fermat

c)

Bernoulli

d)

Laplace

e)

Bayes

3.

The union of events A and B is defined as:

a)

Only A occurs

b)

Only B occurs

c)

Both A and B occur together

d)

A or B occur

e)

Neither A nor B occurs

4.

The intersection of two events A and B means:

a)

Only A occurs

b)

Only B occurs

c)

Both A and B occur together

d)

Either A or B occurs

e)

A occurs but B does not

5.

The difference of events A and B (A \ B) means:

a)

Only A occurs

b)

Only B occurs

c)

Both A and B occur

d)

Either A or B occurs

e)

Neither A nor B occurs

6.

What is combinatorics?

a)

Branch of mathematics about geometric shapes

b)

Branch of mathematics about counting arrangements

c)

Branch of mathematics about continuous functions

d)

Branch of mathematics about equations

e)

Branch of mathematics about probabilities only

7.

If events A and B are mutually exclusive, then the probability of their union equals:

a)

P(A∪B) = P(A) + P(B) - P(A∩B)

b)

P(A∪B) = P(A) × P(B)

c)

P(A∪B) = P(A) + P(B)

d)

P(A∪B) = P(A)/P(B)

e)

P(A∪B) = P(A) - P(B)

8.

What are events called if the occurrence of one excludes the occurrence of the other?

a)

Independent events

b)

Compatible events

c)

Mutually exclusive events

d)

Dependent events

e)

Complementary events

9.

If events A and B are independent, the probability of their joint occurrence equals:

a)

P(A∩B) = P(A) + P(B)

b)

P(A∩B) = P(A) × P(B)

c)

P(A∩B) = P(A|B) × P(B)

d)

P(A∩B) = P(A) / P(B)

e)

P(A∩B) = P(A) - P(B)

10.

What is meant by the conditional probability of event A given that event B has occurred?

a)

P(A|B) = P(A∩B) × P(B)

b)

P(A|B) = P(A∪B)/P(B)

c)

P(A|B) = P(A∩B)/P(B)

d)

P(A|B) = P(A) + P(B)

e)

P(A|B) = P(A) × P(B)

11.

The probability of a certain (sure) event is:

a)

0

b)

0.5

c)

1

d)

Between 0 and 1

e)

Undefined

12.

If an urn contains 9 red, 6 yellow, and 5 green balls, the probability of drawing a red ball is:

a)

9/15

b)

6/20

c)

5/20

d)

9/20

e)

15/20

13.

Out of 1000 televisions, 5 are defective. The probability of selecting a working TV is:

a)

0.005

b)

0.05

c)

0.5

d)

0.95

e)

0.995

14.

In a tournament with 16 teams divided into 4 groups by drawing lots, the probability that a team enters group B is:

a)

1/16

b)

1/8

c)

1/4

d)

1/2

e)

4

/16

15.

A group of 8 tourists randomly chooses 6 people to go shopping. The probability that tourist D will go is:

a)

1/8

b)

1/4

c)

1/2

d)

3

/4

e)

6/8

16.

In a class of 16 students, including two friends, what is the probability that they end up in the same group of four?

a)

1/16

b)

1/8

c)

1/5

d)

1/4

e)

1/2

17.

The probability of the opposite (complementary) event is calculated by the formula:

a)

P(Ā) = P(A) - 1

b)

P(Ā) = 1 - P(A)

c)

P(Ā) = P(A) × 2

d)

P(Ā) = P(A)/2

e)

P(Ā) = 0

18.

If a clock's hand stops randomly, the probability that it points between 6 and 9 is:

a)

1/12

b)

1/6

c)

1/4

d)

1/3

e)

1/2

19.

The probability of mutually exclusive events equals:

a)

P(A∪B) = P(A) × P(B)

b)

P(A∪B) = P(A) + P(B) - P(A∩B)

c)

P(A∪B) = P(A) + P(B)

d)

P(A∪B) = P(A|B) × P(B)

e)

P(A∪B) = 1 - P(A∩B)

20.

The sum of probabilities of all elementary outcomes equals:

a)

0

b)

0.5

c)

1

d)

The number of outcomes

e)

Infinity

21.

Which of the following events are mutually exclusive?

a)

Drawing a red card and a king from a deck

b)

Getting heads and tails on two coin tosses

c)

Rolling a 1 and rolling an even number on one die

d)

Head and tail in a single coin toss

e)

Rain and sunshine on the same day

22.

In the geometric definition of probability, the measure of the region represents:

a)

Only area

b)

Only length

c)

Only volume

d)

Area, length or volume

e)

Time only

23.

Which of the following statements are true for geometric probability?

a)

Probability = favorable outcomes / total outcomes

b)

Probability = favorable measure / total measure

c)

Probability = length × width

d)

Probability = area × volume

e)

Probability = time / space

24.

In which areas of science is combinatorics applied?

a)

Only in pure mathematics

b)

Only in physics

c)

Probability theory, computer science

d)

Only in statistics

e)

Only in engineering

25.

Choose correct statements about unrepeatable combinations (dials):

a)

Cₙᵏ = n! × k!

b)

Cₙᵏ = n! / (k!(n−k)!)

c)

Cₙᵏ = (n−k)! / k!

d)

Cₙᵏ = n! / k!

e)

Cₙᵏ = (n+k)! / (n!k!)

26.

What are mutually exclusive events?

a)

Events that always occur together

b)

Events that cannot occur together

c)

Events that are independent

d)

Events that have the same probability

e)

Events that are complementary

27.

What is true for equally likely outcomes?

a)

They have different probabilities

b)

Each has the same probability

c)

They are mutually exclusive only

d)

They are independent only

e)

They are always certain

28.

What characterizes a random event?

a)

It always occurs

b)

It never occurs

c)

It may or may not occur

d)

It has probability 1

e)

It has probability 0

29.

Repeated combinations are used when:

a)

Elements cannot repeat in selections

b)

Order matters

c)

Elements can repeat in selections

d)

Only two elements are selected

e)

All elements must be selected

30.

The addition theorem of probability is used when:

a)

Finding probability of intersection of events

b)

Finding probability of union of events

c)

Finding conditional probability

d)

Finding probability of independent events

e)

Finding probability of complementary events

31.

The formula of total probability is used when:

a)

Events are mutually exclusive

b)

Event can occur through several hypotheses

c)

Events are independent

d)

Finding conditional probability

e)

Events are equally likely

32.

The total probability formula is:

a)

P(A) = ΣP(Hᵢ) + P(A|Hᵢ)

b)

P(A) = ΣP(Hᵢ)P(A|Hᵢ)

c)

P(A) = ΣP(Hᵢ) × P(Hᵢ|A)

d)

P(A) = ΣP(A) × P(Hᵢ)

e)

P(A) = 1 - ΣP(Hᵢ)

33.

The multiplication theorem is used when:

a)

Finding probability of union of events

b)

Finding probability of complementary events

c)

Finding probability of both A and B

d)

Finding probability of either A or B

e)

Finding total probability

34.

What characterizes dependent events?

a)

One event affects the probability of another

b)

Events have no effect on each other

c)

Events cannot occur together

d)

Events always occur together

e)

Events are equally likely

35.

When are events considered dependent?

a)

When they are mutually exclusive

b)

When one affects the probability of the other

c)

When they have the same probability

d)

When they are complementary

e)

When they are equally likely

36.

The probability of an impossible event is:

a)

0

b)

0.5

c)

1

d)

Between 0 and 1

e)

Undefined

37.

The sum of all probabilities in a complete group of events equals:

a)

0

b)

0.5

c)

1

d)

The number of events

e)

Infinity

38.

The number of diagonals in a convex 12-sided polygon equals:

a)

48

b)

50

c)

52

d)

54

e)

56

39.

If P(A) = 0.3, what is the probability of the complementary event Ā?

a)

0.3

b)

0.5

c)

0.7

d)

0.9

e)

1.3

40.

The probability of getting an even number on two dice:

a)

1/6

b)

1/4

c)

1/3

d)

1/2

e)

2/3

41.

Independent events satisfy:

a)

P(A∩B) = P(A) + P(B)

b)

P(A∩B) = P(A) × P(B)

c)

P(A∩B) = P(A|B) × P(B)

d)

P(A∩B) = 0

e)

P(A∩B) = 1 - P(A∪B)

42.

Dependent events satisfy:

a)

P(A∩B) = P(A) × P(B)

b)

P(A∩B) = P(A) × P(B|A)

c)

P(A∩B) = P(A) + P(B)

d)

P(A∩B) = 0

e)

P(A∩B) = 1

43.

Complementary event satisfies:

a)

P(Ā) = P(A) - 1

b)

P(Ā) = 1 - P(A)

c)

P(Ā) = P(A) × 2

d)

P(Ā) = P(A)/2

e)

P(Ā) = 0

44.

Mutually exclusive events satisfy:

a)

P(A∩B) = P(A) × P(B)

b)

P(A∩B) = 0

c)

P(A∩B) = 1

d)

P(A∩B) = P(A) + P(B)

e)

P(A∩B) = P(A|B) × P(B)

45.

Geometric probability formula is:

a)

P = favorable outcomes / total outcomes

b)

P = favorable area / total area

c)

P = length × width

d)

P = time / space

e)

P = volume × density

46.

The main problems of combinatorics are related to:(3)

a)

Counting possible outcomes

b)

Solving differential equations

c)

Building combinations

d)

Building permutations

e)

Calculating integrals

47.

Which of the following statements are true for mutually exclusive events?(2)

a)

They cannot occur together

b)

P(A∩B) = 0

c)

P(A∪B) = P(A) + P(B)

d)

They are always independent

e)

P(A|B) = P(A)

48.

Which of the following statements are true for compatible events?(2)

a)

They can occur together

b)

P(A∩B) = 0

c)

P(A∪B) = P(A) + P(B) − P(A∩B)

d)

They are always independent

e)

They are always mutually exclusive

49.

Which properties are satisfied by the geometric definition of probability?(2)

a)

Mutual exclusiveness

b)

Countability

c)

Independence

d)

Proportionality of measures

e)

Continuity

50.

Which of the following are examples or applications of repeated combinations?(3)

a)

Permutations of distinct objects

b)

Passwords with repeated symbols

c)

Combinations with repetition

d)

Ice cream flavor combinations with repeats allowed

e)

Selecting a committee without replacement

51.

Which are examples of mutually exclusive events?(2)

a)

Drawing a red card and a king

b)

Getting 1 and 2 on one die

c)

Rain and sunshine at the same time

d)

Head and tail on one toss

e)

Winning and losing the same game

52.

Total probability hypotheses must be:(2)

a)

Exhaustive

b)

Independent

c)

Equally likely

d)

Continuous

e)

Mutually exclusive

53.

Certain event:(2)

a)

Occurs in every trial

b)

May or may not occur

c)

P = 1

d)

Never occurs

e)

P = 0

54.

Impossible event:(2)

a)

Never occurs

b)

P = 0

c)

Occurs in every trial

d)

May or may not occur

e)

P = 1

55.

Examples of classical probability definition:(3)

a)

Rolling dice

b)

Coin toss

c)

Stock market analysis

d)

Weather prediction

e)

Card drawing

56.

An example of a combinatorial problem is:(3)

a)

Arranging students

b)

Calculating derivatives

c)

Solving equations

d)

Selecting teams

e)

Creating passwords

57.

Which of the following are equally likely events?(3)

a)

Tossing a fair coin

b)

Rolling a fair die

c)

Choosing one card from a well-shuffled deck

d)

Predicting tomorrow's weather

e)

Winning the lottery

58.

Indicate the characteristics of elementary events:(3)

a)

Equally likely

b)

Cannot be divided further

c)

Mutually exclusive

d)

Always independent

e)

Always certain

59.

The probability of a certain (sure) event is:(1)

a)

0

b)

0.5

c)

1

d)

between 0 and 1

e)

Undefined

60.

Examples of classical probability definition:(3)

a)

Card drawing

b)

Rolling dice

c)

Coin toss

d)

Total probability theorem

e)

Geometric probability

61.

Equally likely examples:(3)

a)

Fair coin

b)

Fair die

c)

Well-shuffled deck of cards

d)

Loaded die

e)

Biased coin

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