Introduction to Probability: Master the Fundamentals of Chance and Uncertainty

Question 1

When you roll a fair six-sided die, what is the probability of obtaining a 6?

Accepted Answer

1/6

Answer

1/3

Answer

1/2

Answer

6/36

Question 2

Which of the following is NOT a property of the multiplication rule of probability?

Accepted Answer

It applies to both dependent and independent events.

Answer

It is used to calculate the probability of the intersection of two events.

Answer

It can be used to find the probability of the union of two events.

Answer

It is based on the fundamental counting principle.

Question 3

Which of the following is NOT a method for computing probability?

Accepted Answer

De Morgan's law

Answer

Theoretical method

Answer

Axiomatic method

Answer

Relative frequency method

Question 4

In a sample space, what is the complement of event A?

Accepted Answer

The set of all outcomes that are not in event A

Answer

The set of all outcomes that are both in event A and its complement

Answer

The set of all outcomes that are neither in event A nor its complement

Answer

The set of all outcomes that are in event A

Question 5

A bag contains 4 red balls, 3 blue balls, and 2 green balls. If two balls are drawn at random with replacement, what is the probability of getting two red balls?

Accepted Answer

4/45

Answer

1/9

Answer

3/9

Answer

2/9

Question 6

A fair coin is tossed three times. What is the probability of getting at least one head?

Accepted Answer

7/8

Answer

1/4

Answer

1/8

Answer

1/2

Question 7

A group of students is asked to choose their favorite subject from math, science, and history. 40% chose math, 30% chose science, and 20% chose history. If one student is chosen at random, what is the probability that they chose math or history?

Accepted Answer

0.6

Answer

0.3

Answer

0.4

Answer

0.5

Question 8

A fair six-sided die is rolled twice. Which of the following is the sample space for this experiment?

Accepted Answer

{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

Answer

{1, 2, 3, 4, 5, 6}

Answer

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

Answer

{2, 4, 6} x {2, 4, 6}

Question 9

Two fair coins are tossed simultaneously. What is the probability of getting at least one head?

Accepted Answer

3/4

Answer

1/2

Answer

1/8

Answer

1/4

Question 10

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

Accepted Answer

The probability of an event can be negative.

Answer

The probability of the sample space is 1.

Answer

The probability of the empty set is 0.

Answer

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

Question 11

If the probability of an event occurring is 0.75, what is the probability of the event not occurring?

Accepted Answer

0.25

Answer

1

Answer

0.5

Answer

0.75

Question 12

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

Accepted Answer

The probability of drawing a heart from a deck of cards, given that the previous card drawn was a spade.

Answer

The probability of rolling a 6 on a die.

Question 13

If events A and B are mutually exclusive, what is the probability of both events happening together?

Accepted Answer

0

Answer

0.5

Answer

Cannot be determined

Answer

1

Question 14

What is the addition rule of probability for independent events?

Accepted Answer

P(A or B) = P(A) + P(B)

Answer

P(A or B) = P(A) / P(B)

Answer

P(A or B) = P(A) x P(B)

Answer

P(A or B) = P(A) - P(B)

Question 15

Which of the following is NOT a fundamental concept in probability?

Accepted Answer

Determinism

Answer

Outcome

Answer

Sample space

Answer

Event

Question 16

What is a sample space in probability?

Accepted Answer

The set of all possible outcomes of an experiment.

Answer

The set of all probabilities in an experiment.

Answer

The set of all events in an experiment.

Answer

The set of all favorable outcomes of an experiment.

Question 17

Which of these is an example of an event in a probability experiment?

Accepted Answer

Getting a number greater than 3 when rolling a die.

Answer

The probability of rolling a 6 is 1/6.

Answer

Rolling the die twice in a row.

Answer

Using a fair six-sided die.

Question 18

What does the addition rule of probability tell us?

Accepted Answer

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

Answer

The probability of two independent events happening is the sum of their probabilities.

Question 19

According to the multiplication rule of probability, how do you calculate the probability of two independent events happening?

Accepted Answer

Multiply the probabilities of each individual event.

Answer

Divide the probability of one event by the probability of the other event.

Answer

Add the probabilities of each individual event.

Question 20

A fair six-sided die is rolled twice. What's the probability of getting a 3 on the first roll and a 5 on the second roll?

Accepted Answer

1/36

Answer

1/12

Answer

1/2

Answer

1/6

Question 21

A bag has 5 red balls, 3 blue balls, and 2 green balls. If you pick one ball randomly, what's the probability of getting a blue or green ball?

Accepted Answer

1/2

Answer

3/10

Answer

1/10

Answer

2/10

Question 22

Out of 100 students surveyed, 60 liked math, 40 liked science, and 20 liked both. What's the probability a student only likes math?

Accepted Answer

0.4

Answer

0.2

Answer

0.8

Answer

0.6

Question 23

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

Accepted Answer

3/4

Answer

1/2

Answer

1

Answer

1/4

Question 24

A bag contains 5 red balls and 3 blue balls. What is the probability of drawing a blue ball?

Accepted Answer

3/8

Answer

5/8

Answer

1/3

Answer

1/2

Question 25

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

Accepted Answer

1/6

Answer

1/12

Answer

1/4

Question 26

A card is drawn from a standard deck of 52 cards. What is the probability of drawing a heart or a king?

Accepted Answer

16/52

Answer

13/52

Answer

4/52

Question 27

Two events A and B are independent. If P(A) = 0.4 and P(B) = 0.6, what is P(A and B)?

Accepted Answer

0.24

Answer

1

Answer

0.7

Answer

0.1

Question 28

A box contains 3 red balls, 2 blue balls, and 5 green balls. Two balls are drawn at random without replacement. What is the probability that both balls are red?

Accepted Answer

3/20

Answer

9/100

Answer

3/10

Question 29

A fair coin is tossed four times. What is the probability of getting exactly three heads?

Accepted Answer

1/4

Answer

1/8

Answer

1/16

Answer

1/2

Question 30

A bag contains 5 red balls, 3 blue balls, and 2 green balls. What is the probability of drawing a red ball given that a blue ball has already been drawn (without replacement)?

Accepted Answer

5/9

Answer

3/10

Answer

2/10

Answer

5/10

Question 31

A company produces light bulbs, with 5% being defective. What is the probability that in a sample of 20 bulbs, exactly 2 are defective?

Accepted Answer

0.189

Answer

0.05

Answer

0.0025

Answer

0.95

Question 32

A student takes a multiple-choice test with 10 questions, each with 4 options. Assuming the student guesses randomly, what is the probability of getting at least 5 questions correct?

Accepted Answer

0.0563

Answer

0.5

Answer

0.1

Answer

0.9

Question 33

A box contains 6 red balls, 4 blue balls, and 5 green balls. If one ball is drawn at random, what is the probability of drawing a blue ball?

Accepted Answer

4/15

Answer

3/10

Answer

1/3

Answer

2/5

Question 34

A coin is tossed twice. What is the probability of getting heads on both tosses?

Accepted Answer

1/4

Answer

1/16

Answer

1/8

Answer

1/2

Question 35

A bag contains 5 red marbles, 4 blue marbles, and 3 green marbles. Two marbles are drawn at random without replacement. What is the probability of drawing a red marble and then a blue marble?

Accepted Answer

20/66

Answer

10/66

Answer

5/66

Answer

15/66

Question 36

A fair six-sided die is rolled. What is the probability of rolling a number greater than 3?

Accepted Answer

1/2

Answer

1/3

Answer

1/4

Question 37

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

Accepted Answer

0.24

Answer

0.48

Answer

0.36

Answer

0.60

Question 38

A bag contains 10 balls, numbered 1 to 10. Two balls are drawn at random with replacement. What is the probability of drawing the ball numbered 5 on the first draw and the ball numbered 7 on the second draw?

Accepted Answer

1/100

Answer

1/10

Answer

1/25

Answer

1/50

Question 39

A box contains 6 red balls, 5 blue balls, and 4 green balls. If two balls are drawn at random with replacement, what is the probability of drawing a blue ball on both draws?

Accepted Answer

25/144

Answer

10/144

Answer

15/144

Question 40

A coin is tossed four times. What is the probability of getting exactly two heads?

Accepted Answer

6/16

Answer

4/16

Answer

3/16

Question 41

A fair dice is rolled twice. What is the probability of getting a sum of 7?

Accepted Answer

1/6

Answer

1/18

Answer

1/12

Question 42

A bag contains 4 red marbles, 3 blue marbles, and 2 green marbles. If three marbles are drawn at random without replacement, what is the probability of drawing a red marble, a blue marble, and a green marble in that order?

Accepted Answer

12/105

Answer

21/105

Answer

18/105

Answer

15/105

Question 43

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. What is the probability of drawing a red or blue marble?

Accepted Answer

10/10

Answer

8/10

Answer

5/10

Answer

3/10

Question 44

A box contains 10 balls, numbered 1 to 10. Two balls are drawn at random without replacement. What is the probability that the sum of the numbers on the balls is even?

Accepted Answer

1/2

Answer

2/5

Answer

1/4

Answer

1/3

Question 45

A fair coin is tossed three times. What is the probability of getting at least one head?

Accepted Answer

7/8

Answer

1/2

Answer

1/8

Answer

3/4

Question 46

A bag contains 4 red marbles, 3 blue marbles, and 2 green marbles. A marble is drawn at random and replaced. What is the probability of drawing a red marble on the second draw?

Accepted Answer

4/9

Answer

1/6

Answer

1/3

Answer

2/3

Question 47

A card is drawn at random from a standard deck of 52 cards. What is the probability of drawing a face card (jack, queen, or king)?

Accepted Answer

3/13

Answer

1/4

Answer

1/2

Answer

1/3

Question 48

Two events, A and B, are independent. If the probability of event A is 0.4 and the probability of event B is 0.6, what is the probability of both events occurring?

Accepted Answer

0.24

Answer

0.48

Answer

0.36

Answer

0.12

Question 49

A bag contains 6 red marbles, 4 blue marbles, and 2 green marbles. Two marbles are drawn at random without replacement. What is the probability that the first marble is red and the second marble is blue?

Accepted Answer

12/75

Answer

24/75

Answer

6/25

Question 50

A fair coin is tossed 10 times. What is the probability of getting exactly 5 heads?

Accepted Answer

252/1024

Answer

1024/252

Answer

128/252

Answer

512/1024