Probability and Chance: Master the Fundamentals with Interactive Quizzes

Question 1

A box contains 10 items, of which 5 are defective. If 3 items are selected at random without replacement, what is the probability of selecting exactly 2 defective items?

Accepted Answer

3/20

Answer

1/20

Answer

3/10

Answer

1/5

Question 2

A die is rolled three times. What is the probability of getting a sum of 12?

Accepted Answer

1/216

Answer

1/18

Answer

1/12

Answer

1/36

Question 3

A bag contains 4 green balls, 3 red balls, and 2 blue balls. If a ball is drawn at random, what is the probability that it is not green?

Accepted Answer

1/2

Answer

1/3

Answer

1/4

Question 4

A research study found that the average number of hours spent studying per week by students in a particular college is 12, with a standard deviation of 2. If a student is randomly selected from this college, what is the probability that they spend more than 15 hours studying per week? Assume the distribution is normal.

Accepted Answer

0.1587

Answer

0.3413

Answer

0.4772

Question 5

A standard deck of 52 cards has 4 suits: hearts, diamonds, clubs, and spades. Each suit has 13 cards. What is the probability of drawing a heart from a well-shuffled deck?

Accepted Answer

1/4

Answer

1/52

Answer

1/13

Question 6

A coin is tossed 3 times. What is the probability of getting at least one head?

Accepted Answer

7/8

Answer

1/8

Answer

3/8

Answer

1/2

Question 7

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If one marble is drawn at random, what is the probability of drawing a blue marble?

Accepted Answer

3/10

Answer

2/10

Answer

3/5

Answer

1/2

Question 8

A coin is flipped 4 times. What is the probability of getting exactly two heads?

Accepted Answer

3/8

Answer

1/4

Answer

1/2

Answer

1/8

Question 9

A company produces light bulbs with a 1% defect rate. If a sample of 100 bulbs is chosen randomly, what is the approximate probability that at least 2 bulbs are defective? Assume the defects occur independently.

Accepted Answer

0.264

Answer

0.01

Answer

0.095

Answer

0.99

Question 10

The average number of cars passing a certain point on a highway in an hour is 10. What is the probability of exactly 5 cars passing the point in a given hour? Assume the arrivals of cars follow a Poisson distribution.

Accepted Answer

0.037

Answer

0.01

Answer

0.1

Answer

0.5

Question 11

A bag contains 5 red balls, 3 blue balls, and 2 green balls. If a ball is drawn at random, what is the probability of drawing a blue ball?

Accepted Answer

3/10

Answer

1/4

Answer

2/5

Answer

1/2

Question 12

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

Accepted Answer

1/2

Answer

1/4

Answer

1/6

Answer

1/3

Question 13

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

Accepted Answer

13/26

Answer

1/2

Answer

1/4

Answer

3/8

Question 14

A survey is conducted among 100 students to determine their favorite subject. The results show that 30 students like math, 40 students like science, and 20 students like both math and science. What is the probability that a randomly selected student likes math given that they do not like science?

Accepted Answer

1/2

Answer

1/3

Answer

1/4

Answer

2/5

Question 15

A bag contains 4 red marbles, 3 blue marbles, and 2 green marbles. Three marbles are drawn at random, one after the other, without replacement. What is the probability that the first marble is red, the second marble is blue, and the third marble is green?

Accepted Answer

12/126

Answer

1/24

Answer

1/12

Answer

1/6

Question 16

A lottery has 1000 tickets. If you buy 5 tickets, what is the probability that you will win the lottery?

Accepted Answer

0.005

Answer

0.1

Answer

0.05

Answer

0.01

Question 17

The probability of a student passing an exam is 0.7. If the student takes the exam twice independently, what is the probability that the student passes both exams?

Accepted Answer

0.49

Answer

0.56

Answer

0.63

Answer

0.72

Question 18

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

Accepted Answer

0.246

Answer

0.123

Answer

0.369

Answer

0.512

Question 19

A normal distribution has a mean of 10 and a standard deviation of 2. What is the probability that a randomly selected value from this distribution is between 8 and 12?

Accepted Answer

0.6827

Answer

0.8185

Answer

0.3173

Answer

0.4713

Question 20

A company has a production process that produces items with a 5% defect rate. If a sample of 20 items is randomly selected, what is the probability that exactly 2 of the items are defective?

Accepted Answer

0.133

Answer

0.081

Answer

0.303

Answer

0.218

Question 21

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

Accepted Answer

3/10

Answer

2/5

Answer

1/3

Answer

1/2

Question 22

A fair coin is flipped 4 times. What is the probability of getting at least one head?

Accepted Answer

15/16

Answer

1/16

Answer

7/8

Answer

1/2

Question 23

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

Accepted Answer

1/6

Answer

1/3

Answer

1/12

Question 24

A box contains 5 apples and 3 oranges. Two fruits are randomly selected without replacement. What is the probability of getting one apple and one orange?

Accepted Answer

15/56

Answer

5/14

Answer

3/8

Answer

1/2

Question 25

A student has to answer 5 multiple-choice questions. Each question has 4 options, only one of which is correct. What is the probability that the student will answer all questions correctly by guessing?

Accepted Answer

1/1024

Answer

1/16

Answer

1/64

Answer

1/256

Question 26

A bag contains 4 red marbles and 6 blue marbles. Two marbles are drawn randomly without replacement. What is the probability that both marbles are red?

Accepted Answer

2/15

Answer

1/3

Answer

1/5

Answer

1/4

Question 27

A company produces light bulbs with a 2% defect rate. What is the probability that in a batch of 100 bulbs, exactly 3 are defective?

Accepted Answer

0.018

Answer

0.2

Answer

0.05

Answer

0.002

Question 28

A survey shows that 70% of students in a college like pizza. If 10 students are randomly selected, what is the expected number of students who like pizza?

Accepted Answer

7

Answer

5

Answer

3

Answer

10

Question 29

The probability of winning a lottery is 1 in 10,000. If 50,000 people participate, how many people are expected to win?

Accepted Answer

5

Answer

50

Answer

1

Answer

10

Question 30

A fair coin is flipped 3 times. What is the probability of getting exactly two heads?

Accepted Answer

3/8

Answer

1/4

Answer

1/2

Question 31

A bag contains 5 red marbles and 3 blue marbles. What is the probability of randomly selecting a blue marble?

Accepted Answer

3/8

Answer

5/3

Answer

3/5

Answer

5/8

Question 32

Two fair dice are rolled. What is the probability that the sum of the numbers shown is 7?

Accepted Answer

1/6

Answer

1/4

Answer

1/12

Answer

1/36

Question 33

A student is randomly guessing answers on a true/false quiz with 5 questions. What is the probability of the student getting all 5 questions correct?

Accepted Answer

1/32

Answer

1/2

Answer

1/5

Answer

1/10

Question 34

Events A and B are mutually exclusive. If P(A) = 0.3 and P(B) = 0.5, what is P(A or B)?

Accepted Answer

0.8

Answer

0.2

Answer

0.15

Question 35

A company produces light bulbs, and 2% of the bulbs are defective. What is the probability that a randomly selected bulb is not defective?

Accepted Answer

0.98

Answer

0.02

Answer

1

Answer

0.96

Question 36

A random variable X has a binomial distribution with n = 10 and p = 0.4. What is the expected value of X?

Accepted Answer

4

Answer

6

Answer

10

Answer

2.5

Question 37

The heights of adult males in a city are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. What is the probability that a randomly selected male is taller than 76 inches?

Accepted Answer

0.0228 (approximately)

Answer

0.5

Answer

1

Answer

0.9772 (approximately)

Question 38

How many different ways can 5 people be arranged in a line?

Accepted Answer

120

Answer

60

Answer

5

Answer

25

Question 39

A committee of 3 people is to be chosen from a group of 8 people. How many different committees are possible?

Accepted Answer

56

Answer

336

Answer

512

Answer

24

Question 40

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

Accepted Answer

0.6

Answer

0.4

Answer

1

Answer

0.24

Question 41

A coin is flipped three times. What is the probability of getting exactly two heads?

Accepted Answer

3/8

Answer

1/8

Answer

1/2

Answer

1/4

Question 42

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

Accepted Answer

3/10

Answer

1/2

Answer

1/3

Answer

1/5

Question 43

A standard deck of 52 cards has 4 suits: hearts, diamonds, clubs, and spades.  What is the probability of drawing a heart?

Accepted Answer

1/4

Answer

1/13

Answer

1/52

Answer

1/2

Question 44

Two fair dice are rolled. What is the probability that the sum of the numbers is 7?

Accepted Answer

1/6

Answer

1/2

Answer

1/36

Answer

1/12

Question 45

A committee of 3 people is to be chosen from a group of 5. How many different committees are possible?

Accepted Answer

10

Answer

60

Answer

20

Answer

15

Question 46

A box contains 4 red balls and 6 blue balls.  Two balls are drawn at random without replacement. What is the probability that both balls are red?

Accepted Answer

2/15

Answer

1/10

Answer

1/4

Answer

1/5

Question 47

A company manufactures light bulbs, and 5% of the bulbs are defective. What is the probability that a randomly selected bulb is not defective?

Accepted Answer

0.95

Answer

0.5

Answer

1

Answer

0.05

Question 48

A bag contains 3 red balls and 2 blue balls. Two balls are drawn at random with replacement. What is the probability that both balls are the same color?

Accepted Answer

13/25

Answer

2/5

Answer

1/2

Answer

3/5

Question 49

A fair coin is flipped 5 times. What is the probability of getting at least one head?

Accepted Answer

31/32

Answer

15/16

Answer

1/2

Answer

1/32

Question 50

A company produces light bulbs with a mean life of 1000 hours and a standard deviation of 100 hours. Assuming a normal distribution, what is the probability that a randomly selected bulb will last longer than 1100 hours?

Accepted Answer

0.1587

Answer

0.5

Answer

0.8413