Probability and Chance: Master the Fundamentals of Probability Theory

Question 1

An experiment consists of rolling a standard six-sided die and observing the number that faces up. What is the probability of rolling **an** even number?

Accepted Answer

1/2

Answer

1/3

Answer

2/3

Answer

3/4

Question 2

A random variable X has a binomial distribution with n = 10 and p = 0.5. What is the probability of getting exactly **5** successes?

Accepted Answer

0.2461

Answer

0.3422

Answer

0.4383

Answer

0.5344

Question 3

A bag contains 4 red balls, 3 blue balls, and 2 green balls. If one ball is drawn from the bag at random, what is the probability of selecting a blue ball?

Accepted Answer

1/3

Answer

1/4

Answer

1/6

Answer

1/8

Question 4

What type of probability distribution is used to model the number of arrivals at a bank in a given hour?

Accepted Answer

Poisson distribution

Answer

Binomial distribution

Answer

Normal distribution

Answer

Exponential distribution

Question 5

A survey found that 60% of students prefer coffee, while 40% prefer tea. What is the probability that a randomly selected student prefers coffee?

Accepted Answer

0.6

Answer

0.4

Answer

0.5

Answer

0.8

Question 6

A fair die is rolled once. What is the probability of rolling a number **greater than 3**?

Accepted Answer

1/2

Answer

1/3

Answer

1/4

Answer

1/5

Question 7

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

Accepted Answer

5/12

Answer

1/2

Answer

5/8

Answer

1/3

Question 8

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

Accepted Answer

3/4

Answer

1/4

Answer

1/2

Answer

1

Question 9

Which of the following is NOT a property of probability?

Accepted Answer

It can be negative.

Answer

It is always between 0 and 1 inclusive.

Answer

The sum of probabilities of all events in a sample space is 1.

Answer

It is additive for mutually exclusive events.

Question 10

A random variable X follows a binomial distribution with n = 5 and p = 0.4. What is the probability of X taking the value 2?

Accepted Answer

0.32

Answer

0.4

Answer

0.48

Answer

0.56

Question 11

A jar contains 10 marbles, numbered from 1 to 10. If two marbles are drawn randomly, with replacement, what is the probability that the sum of the numbers on the marbles is 9?

Accepted Answer

1/9

Answer

2/9

Answer

1/10

Answer

1/5

Question 12

A fair six-sided die is rolled twice. What is the probability of getting a sum that is greater than 9 and less than 12?

Accepted Answer

5/12

Answer

1/6

Answer

1/3

Question 13

A fair coin is flipped four times. What is the probability of getting an even number of tails?

Accepted Answer

1/2

Answer

3/4

Answer

1/4

Answer

0

Question 14

A coin is flipped twice. What is the probability of getting tails on both flips?

Accepted Answer

1 / 4

Answer

3 / 4

Answer

1

Answer

1 / 2

Question 15

A fair six-sided die is rolled. What is the probability of rolling an even number?

Accepted Answer

1 / 2

Answer

1 / 6

Answer

1 / 3

Answer

1 / 4

Question 16

A bag contains 6 marbles: 2 red, 3 blue, and 1 green. If two marbles are drawn without replacement, what is the probability that the first marble drawn is red and the second marble drawn is blue?

Accepted Answer

2 / 15

Answer

1 / 2

Answer

1 / 3

Answer

1 / 6

Question 17

A survey of 100 students found that 60% of them like math and 40% of them like science. If a student is selected at random, what is the probability that they do not like either math or science?

Accepted Answer

0.16

Answer

0.48

Answer

0.36

Answer

0.60

Question 18

A box contains 12 balls, of which 5 are white, 4 are black, and 3 are red. If three balls are drawn at random with replacement, what is the probability of drawing one white ball, one black ball, and one red ball in that order?

Accepted Answer

0.216

Answer

0.144

Answer

0.360

Answer

0.288

Question 19

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

Accepted Answer

0.375

Answer

0.25

Answer

0.5

Answer

0.125

Question 20

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

Accepted Answer

0.3

Answer

0.5

Answer

0.1

Answer

0.2

Question 21

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

1

Answer

0.5

Answer

0.1

Question 22

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

Accepted Answer

13/26

Answer

13/52

Answer

2/13

Answer

1/4

Question 23

A bag contains 4 red balls and 6 blue balls. Two balls are drawn at random, without replacement. What is the probability of drawing one red ball and one blue ball?

Accepted Answer

0.2667

Answer

0.4

Answer

0.6

Answer

0.5

Question 24

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

Accepted Answer

0.9688 (approximately)

Answer

0.5

Answer

0.0312

Answer

1

Question 25

A box contains 3 defective bulbs and 7 non-defective bulbs. Two bulbs are randomly selected, without replacement. What is the probability that both bulbs are defective?

Accepted Answer

0.1

Answer

0.2

Answer

0.3

Answer

0.4

Question 26

A random variable X has the following probability distribution: P(X = 0) = 0.2, P(X = 1) = 0.5, P(X = 2) = 0.3. What is the expected value of X?

Accepted Answer

1

Answer

0.5

Answer

0.2

Answer

2

Question 27

The probability of rain tomorrow is 30%. If it rains, the probability of the baseball game being canceled is 80%. If it doesn't rain, the probability of the game being canceled is 10%. What is the probability that the baseball game will be canceled tomorrow?

Accepted Answer

0.26

Answer

0.08

Answer

0.34

Answer

0.18

Question 28

A standard deck of 52 cards has four aces and four kings.  If you draw two cards at random without replacing the first card, what is the probability of drawing an ace followed by a king?

Accepted Answer

4/221

Answer

1/26

Answer

1/52

Answer

1/104

Question 29

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

Accepted Answer

Probability can be negative.

Answer

Probability is a measure of the likelihood of an event occurring.

Answer

Probability is additive for mutually exclusive events.

Answer

Probability is a number between 0 and 1.

Question 30

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

Accepted Answer

1/2

Answer

3/10

Answer

2/10

Answer

1/10

Question 31

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

Accepted Answer

1/6

Answer

5/36

Answer

4/36

Answer

3/36

Question 32

A fair coin is flipped ten times.  What is the probability of getting exactly five heads?

Accepted Answer

252/1024

Answer

126/1024

Answer

512/1024

Answer

63/1024

Question 33

A survey of 100 students found that 60% liked math and 40% liked science. If a student is randomly chosen, what is the probability that they like both math and science?

Accepted Answer

0.24

Answer

0.36

Answer

0.48

Answer

0.60

Question 34

A random variable X follows a normal distribution with a mean of 50 and a standard deviation of 10. What is the probability that X is between 40 and 60?

Accepted Answer

0.6827

Answer

0.8413

Answer

0.3173

Answer

0.5000

Question 35

In a standard deck of 52 cards, what is the probability of drawing either an ace or a king?

Accepted Answer

1/13

Answer

1/8

Answer

1/26

Answer

1/2

Question 36

A bag contains 5 white balls and 3 black balls. Two balls are drawn without replacement.  What is the probability that both balls are white?

Accepted Answer

5/14

Answer

1/2

Answer

2/3

Answer

1/6

Question 37

What is the expected value of a random variable X that takes on the values 1, 2, and 3 with probabilities 1/4, 1/2, and 1/4, respectively?

Accepted Answer

2

Answer

3

Answer

4

Answer

1

Question 38

A company claims that its product has a 95% success rate. If the product is used independently 10 times, what is the probability of at least 9 successes?

Accepted Answer

0.9990

Answer

0.5625

Answer

0.9050

Answer

0.0950

Question 39

A 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 40

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

1/3

Answer

1/2

Answer

1/5

Question 41

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

Accepted Answer

1/6

Answer

1/4

Answer

1/3

Answer

1/12

Question 42

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

Accepted Answer

16/52

Answer

13/52

Answer

4/52

Question 43

A coin is flipped 5 times. What is the probability of getting exactly 3 heads?

Accepted Answer

10/32

Answer

1/32

Answer

5/32

Answer

1/2

Question 44

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

Accepted Answer

2/15

Answer

4/15

Answer

1/10

Answer

1/5

Question 45

A company produces light bulbs with a 1% chance of being defective. What is the probability that a sample of 100 light bulbs will have at least one defective bulb?

Accepted Answer

approximately 63.4%

Answer

approximately 99%

Answer

approximately 1%

Question 46

A random variable X has the following probability distribution: P(X = 1) = 0.2, P(X = 2) = 0.3, P(X = 3) = 0.5. What is the expected value of X?

Accepted Answer

2.2

Answer

3.0

Answer

2.5

Answer

1.5

Question 47

A fair coin is tossed 10 times. What is the most likely number of heads to occur?

Accepted Answer

5

Answer

10

Answer

0

Answer

6

Question 48

A bag contains 3 red balls and 2 blue balls. Two balls are drawn randomly without replacement. What is the probability that the second ball drawn is red, given that the first ball drawn is blue?

Accepted Answer

3/4

Answer

3/5

Answer

1/2