Probability and Chance: Master the Fundamentals of Probability

Question 1

Which of the following is NOT a property of a probability distribution function (PDF)?

Accepted Answer

The PDF of a continuous random variable is a discrete function

Answer

The area under the curve of a PDF is always positive

Answer

The integral of a PDF over the entire real line is 1

Answer

The sum of the probabilities of all possible outcomes is 1

Question 2

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

Accepted Answer

3/4

Answer

1/2

Answer

1/4

Answer

1/8

Question 3

Which of the following statements about the standard normal distribution is accurate?

Accepted Answer

It has a mean of 0 and a standard deviation of 1

Answer

It is skewed to the left

Answer

Its area under the curve is always greater than 0.5

Answer

It is a discrete distribution

Question 4

When rolling a standard six-sided die twice, what's the chance that the total of the two rolls will be higher than 8?

Accepted Answer

5 in 36

Answer

1 in 12

Answer

1 in 2

Answer

2 in 3

Question 5

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

3/4

Answer

15/16

Question 6

The probability of an event A occurring is 0.4 and the probability of event B occurring is 0.6. If the events are mutually exclusive, what is the probability of either A or B occurring?

Accepted Answer

1.00

Answer

0.24

Answer

0.60

Answer

1.60

Question 7

The probability of an event happening is 0.3. What is the probability of the event not happening?

Accepted Answer

0.7

Answer

0.3

Answer

0.6

Answer

1.0

Question 8

A survey found that 40% of people prefer tea, while 60% prefer coffee. If 100 people are randomly selected, what is the expected number of people who prefer tea?

Accepted Answer

40

Answer

60

Answer

100

Answer

200

Question 9

A survey of 100 students showed that 60 liked math and 40 liked science. If 20 students liked both math and science, what is the probability that a randomly selected student likes only math?

Accepted Answer

2/5

Answer

1/2

Answer

1/3

Answer

1/4

Question 10

What is the probability of rolling a number greater than 3 on a standard six-sided die?

Accepted Answer

2/3

Answer

1/3

Answer

1/2

Answer

3/6

Question 11

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

Accepted Answer

3/16

Answer

1/4

Answer

1/8

Answer

1/16

Question 12

Which of the following is NOT an assumption of the normal distribution?

Accepted Answer

Data is categorical

Answer

Data is symmetrically distributed

Answer

Data follows a bell-shaped curve

Answer

Mean and standard deviation are known

Question 13

A random variable X has a binomial distribution with n = 6 and p = 0.4. What is the probability of X taking the value 3?

Accepted Answer

0.2048

Answer

0.3328

Answer

0.4536

Answer

0.5784

Question 14

What is the primary purpose of Bayes' theorem?

Accepted Answer

Calculating the probability of an event based on the occurrence of another event

Answer

Determining the probability of an event based on its observed frequency

Answer

Finding the mean of a probability distribution

Answer

Calculating the variance of a probability distribution

Question 15

Determine the mean of a Poisson distribution with a parameter of 5.

Accepted Answer

5

Answer

2

Answer

7

Answer

10

Question 16

Which of the following is an example of a continuous probability distribution?

Accepted Answer

Normal distribution

Answer

Binomial distribution

Answer

Poisson distribution

Answer

Uniform distribution

Question 17

What is the expected value of a random variable X?

Accepted Answer

The mean value of X

Answer

The most common value of X

Answer

The lowest value of X

Answer

The highest value of X

Question 18

A coin is tossed 4 times. What is the probability of getting exactly 2 heads?

Accepted Answer

6/16

Answer

1/2

Answer

1/8

Answer

1/4

Question 19

A bag contains 10 balls, numbered 1 to 10. If three balls are drawn randomly, with replacement, what is the probability that they are all odd numbers?

Accepted Answer

5/27

Answer

1/9

Answer

1/27

Answer

1/3

Question 20

A box contains 6 red balls and 4 blue balls. If two balls are drawn randomly, with replacement, what is the probability that they are both the same color?

Accepted Answer

10/27

Answer

1/18

Answer

1/3

Answer

1/9

Question 21

A survey of 100 people found that 60% of them like coffee and 40% of them like tea. If 20% of them like both coffee and tea, what percentage of them like only coffee?

Accepted Answer

28%

Answer

60%

Answer

80%

Answer

40%

Question 22

Bayes' theorem states that:

Accepted Answer

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

Answer

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

Answer

P(A ∩ B) = P(A) + P(B) - P(A ∪ B)