Probability and Chance: Master the Fundamentals of Probability

Question 1

A bag contains 5 red, 3 blue, and 2 green balls. If two balls are drawn randomly without replacement, what is the probability that the first ball is red and the second ball is blue?

Accepted Answer

5/10 * 3/10

Answer

5/10 * 3/9

Answer

5/10 * 2/9

Answer

5/10 * 2/10

Question 2

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

Accepted Answer

7/8

Answer

1/2

Answer

3/4

Answer

1

Question 3

In a bag containing 6 red balls and 4 blue balls, what is the probability of selecting a red ball?

Accepted Answer

0.6

Answer

0.4

Answer

0.5

Answer

0.8

Question 4

A survey of 100 people found that 60% liked dogs and 40% liked cats. If 20% of the people liked both dogs and cats, what percentage of people liked only dogs?

Accepted Answer

28%

Answer

40%

Answer

52%

Answer

64%

Question 5

Two cards are drawn **without replacement** from a standard deck of 52 cards. What is the probability that both cards are red?

Accepted Answer

1/26

Answer

1/13

Answer

1/4

Answer

1/8

Question 6

What is the area under the normal distribution curve between z-scores of -1 and 1?

Accepted Answer

0.6827

Answer

0.3413

Answer

0.9545

Answer

0.9973

Question 7

What is the probability of rolling a six on a standard six-sided die?

Accepted Answer

1/6

Answer

1/2

Answer

1/3

Answer

1/4

Question 8

Which of the following is a conditional probability?

Accepted Answer

P(A | B)

Answer

P(A)

Answer

P(A and B)

Answer

P(A or B)

Question 9

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If a marble is drawn at random from the bag, what is the probability that it is not blue?

Accepted Answer

4/5

Answer

1/2

Answer

2/5

Answer

3/5

Question 10

What is the mean of a Poisson distribution with parameter λ?

Accepted Answer

λ

Answer

λ/2

Answer

2λ

Answer

√λ

Question 11

What is the probability density function of a normal distribution with mean μ and standard deviation σ?

Accepted Answer

1/(σ√(2π)) * e^(-(x-μ)^2/(2σ^2))

Answer

1/(2πσ^2) * e^(-(x-μ)^2/(2))

Answer

1/σ * e^(-(x-μ)^2)

Answer

1/√(2π) * e^(-(x-μ)^2)

Question 12

Which of the following is not an assumption of the central limit theorem?

Accepted Answer

The population is finite

Answer

The sample size is large

Answer

The population is normally distributed

Answer

The trials are independent

Question 13

The expected value of a random variable X is defined as:

Accepted Answer

The average value of X

Answer

The sum of the probabilities of all possible outcomes of X

Answer

The most likely outcome of X

Answer

The probability that X will take a particular value

Question 14

A box contains six balls labeled 1 to 6. If two balls are drawn without replacement, what is the probability of drawing an even number on the first draw and an odd number on the second draw?

Accepted Answer

1/12

Answer

1/6

Answer

1/15

Answer

1/18

Question 15

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

Accepted Answer

15/16

Answer

1/2

Answer

1/4

Answer

3/4

Question 16

What is the likelihood of rolling a '6' when tossing a standard six-sided die?

Accepted Answer

1/6

Answer

1/2

Answer

1/3

Answer

1/4

Question 17

Which formula represents Bayes' theorem?

Accepted Answer

P(A|B) = P(B|A) * P(A) / P(B)

Answer

P(A|B) = P(B|A) / P(A)

Answer

P(A|B) = P(A) * P(B) / P(B|A)

Answer

P(A|B) = P(B|A) * P(A)

Question 18

Which measure of central tendency is most appropriate for skewed data?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Answer

Range

Question 19

A bag contains 5 red marbles and 7 blue marbles. If one marble is drawn at random, what is the probability that it is red given that it is not blue?

Accepted Answer

1/2

Answer

1/3

Answer

1/4

Answer

1/5

Question 20

A survey found that 60% of students prefer chocolate ice cream, 25% prefer vanilla, and 15% prefer strawberry. If a student is selected randomly, what is the probability that they do not prefer chocolate ice cream?

Accepted Answer

0.4

Answer

0.6

Answer

0.15

Question 21

A survey of 100 students revealed that 60 study Mathematics, 40 study Science, and 20 study both Mathematics and Science. What is the probability that a randomly selected student studies Mathematics or Science?

Accepted Answer

80/100

Answer

20/100

Answer

40/100

Answer

60/100

Question 22

A continuous random variable X has the following probability density function:

f(x) = 2x for 0 ≤ x ≤ 1

What is the probability that X is greater than 0.5?

Accepted Answer

3/4

Answer

1/2

Answer

1/4

Answer

1/8

Question 23

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

Accepted Answer

7/8

Answer

1/8

Answer

1/2

Answer

3/4

Question 24

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

Accepted Answer

3/10

Answer

1/2

Answer

1/4

Answer

1/8

Question 25

If three fair coins are tossed, what is the probability of getting exactly two heads?

Accepted Answer

3/8

Answer

1/8

Answer

1/2

Answer

1/4

Question 26

A dice is rolled. What is the probability of getting a number less than 3?

Accepted Answer

1/3

Answer

1/2

Answer

1/6

Answer

1/4

Question 27

A box contains 5 red cards, 3 blue cards, and 7 green cards. A card is drawn at random. What is the probability of drawing a red card, given that the card is not green?

Accepted Answer

5/8

Answer

3/8

Answer

1/8

Answer

1/2

Question 28

A coin is tossed 10 times. What is the expected number of times it will land on heads?

Accepted Answer

5

Answer

8

Answer

2

Answer

10

Question 29

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

Accepted Answer

3/10

Answer

1/5

Answer

1/3

Answer

1/2

Question 30

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

Accepted Answer

1/4

Answer

1/8

Answer

1/2

Answer

1/3

Question 31

A bag contains 6 balls numbered 1 to 6. Two balls are drawn from the bag without replacement. What is the probability that the sum of the numbers on the two balls is 7?

Accepted Answer

1/5

Answer

1/3

Answer

1/10

Answer

1/6

Question 32

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

Answer

1/6

Question 33

A box contains 100 balls: 30 red, 40 blue, and 30 green. Two balls are drawn at random with replacement. What is the probability of drawing a red ball followed by a blue ball?

Accepted Answer

12/25

Answer

3/5

Answer

9/25

Answer

2/5

Question 34

A survey found that 60% of people prefer coffee, and 40% prefer tea. If 100 people are randomly selected, what is the approximate probability that more than 50 people prefer coffee?

Accepted Answer

0.988

Answer

0.954

Answer

0.904

Answer

0.841

Question 35

A card is randomly drawn from a standard deck of 52 cards. What is the probability that the card is either a heart or a diamond?

Accepted Answer

1/2

Answer

1/3

Answer

1/4

Answer

1/6

Question 36

A company claims their product will last at least 5 years. The probability of the product failing before 5 years is 0.1. What is the probability that the product will last at least 5 years?

Accepted Answer

0.9

Answer

0.7

Answer

0.8

Answer

0.6

Question 37

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

Accepted Answer

7/8

Answer

3/4

Answer

1/2

Answer

1/4

Question 38

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

0.36

Answer

0.16

Answer

0.48