Probability for Engineering Mathematics: Master Your Concepts with Quizzes

Question 1

Which of the following statements is NOT among the axioms of probability theory?

Accepted Answer

The probability of any event is at most 0.5.

Answer

The probability of an event cannot be less than zero.

Answer

The probability of the sample space is always equal to 1.

Answer

The sum of the probabilities of all mutually exclusive events is 1.

Question 2

Which of the following is a non-probability sampling technique?

Accepted Answer

Convenience sampling

Answer

Simple random sampling

Answer

Stratified sampling

Answer

Systematic sampling

Question 3

Which of the following is NOT an axiom of probability theory?

Accepted Answer

The probability of the intersection of two disjoint events is equal to the sum of their probabilities.

Answer

The probability of an event is a non-negative real number.

Answer

The probability of the sample space is equal to 1.

Answer

The probability of an impossible event is equal to 0.

Question 4

A fair coin is flipped twice. What is the probability of getting tails on the first flip and heads on the second flip?

Accepted Answer

1/4

Answer

1/2

Answer

1

Answer

0

Question 5

In probability, the conditional probability of event A given event B is denoted as P(A|B). Which of the following formulas correctly defines P(A|B)?

Accepted Answer

P(A|B) = P(A ∩ B) / P(B)

Answer

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

Answer

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

Question 6

Which of the following statements is NOT an axiom of probability?

Accepted Answer

The probability of the sample space is 0

Answer

The probability of an event cannot be negative

Answer

The probability of an event and its complement is 1

Answer

The probability of two mutually exclusive events is the sum of their probabilities

Question 7

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

Accepted Answer

0.25

Answer

0.5

Answer

0.75

Answer

1

Question 8

Which of the following is the formula for Bayes' theorem?

Accepted Answer

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

Answer

P(A|B) = P(B|A) * P(A) - P(B|not A) * P(not A)

Answer

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

Answer

P(A|B) = P(B|A) / P(A|not B)

Question 9

Which of the following is an example of a discrete random variable?

Accepted Answer

Number of siblings in a family

Answer

Height of a tree

Answer

Lifetime of a light bulb

Answer

Temperature on a given day

Question 10

Which of the following is an axiom of probability?

Accepted Answer

The probability of an event cannot exceed 1.

Answer

The probability of an event is always negative.

Answer

The probability of the sample space is less than 1.

Answer

The probability of the intersection of two events is always greater than the probability of either event.

Question 11

Bayes' theorem is used to:

Accepted Answer

Calculate the conditional probability of an event.

Answer

Calculate the probability of an event based on its complement.

Answer

Calculate the expected value of a random variable.

Answer

Calculate the variance of a random variable.

Question 12

Which of the following is a continuous probability distribution?

Accepted Answer

Exponential distribution

Answer

Binomial distribution

Answer

Poisson distribution

Answer

Hypergeometric distribution

Question 13

Which of the following statistical techniques is used to test hypotheses about a population?

Accepted Answer

Hypothesis testing

Answer

Point estimation

Answer

Interval estimation

Answer

Regression analysis

Question 14

Which of the following is not an axiom of probability?

Accepted Answer

The probability of an event equals the ratio of favorable outcomes to total possible outcomes.

Answer

The probability of an event can range from 0 to 1.

Answer

The probability of the entire sample space is 1.

Answer

The probability of the union of disjoint events equals the sum of their probabilities.

Question 15

What is the probability of obtaining a 6 when rolling a fair six-sided die?

Accepted Answer

1/6

Answer

1/5

Answer

1/4

Answer

1/3

Question 16

What is Bayes' theorem used for?

Accepted Answer

Calculating the probability of an event based on prior probability and known evidence.

Answer

Calculating the probability of an event based on conditional probabilities of outcomes.

Answer

Calculating the probability of an event based on the number of outcomes in the sample space.

Answer

Calculating the probability of an event based on the results of a random experiment.

Question 17

Which of the following is a continuous probability distribution?

Accepted Answer

Normal distribution

Answer

Discrete uniform distribution

Answer

Binomial distribution

Answer

Poisson distribution

Question 18

Which of the following is a measure of the spread of a probability distribution?

Accepted Answer

Variance

Answer

Mean

Answer

Median

Answer

Mode

Question 19

What is the difference between a parameter and a statistic?

Accepted Answer

A parameter is a fixed population characteristic, while a statistic is a random sample characteristic.

Answer

A parameter is a random sample characteristic, while a statistic is a fixed population characteristic.

Answer

A parameter describes a population, while a statistic describes a sample.

Answer

A statistic describes a population, while a parameter describes a sample.

Question 20

For a given event A, what is its complement?

Accepted Answer

The event that A does not occur.

Answer

The event that either A or its complement occur.

Answer

The event that both A and its complement occur.

Answer

An event that is independent of A.

Question 21

Which theorem is commonly used to update probabilities in light of new evidence?

Accepted Answer

Bayes' theorem

Answer

Central Limit Theorem

Answer

Law of Large Numbers

Answer

Binomial Theorem

Question 22

Select the option that does not accurately describe a continuous random variable:

Accepted Answer

It assumes discrete values.

Answer

It can take any value within a specified range.

Answer

Its probability is defined by a probability density function.

Answer

Its cumulative distribution function provides the probability of it taking a value less than or equal to a given value.

Question 23

Which statistical measure describes the typical value of a dataset?

Accepted Answer

Mean

Answer

Variance

Answer

Skewness

Answer

Kurtosis

Question 24

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

Accepted Answer

3/4

Answer

1/4

Answer

1/2

Answer

1

Question 25

Let X and Y be two independent random variables with probability mass functions f(x) and g(y), respectively. What is the joint probability mass function of X and Y?

Accepted Answer

f(x) * g(y)

Answer

f(x) + g(y)

Answer

f(x) / g(y)

Answer

g(x) * f(y)

Question 26

Which of the following is Bayes' theorem?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 27

Which of the following is a measure of the spread or variability of a probability distribution?

Accepted Answer

Variance

Answer

Mean

Answer

Median

Answer

Mode

Question 28

Which of the following is NOT an axiom of probability?

Accepted Answer

The probability of the intersection of two mutually exclusive events is their sum.

Answer

The probability of an event cannot be negative or greater than 1.

Answer

The sum of the probabilities of all possible outcomes in a sample space equals 1.

Answer

The probability of the complement of an event is the difference between 1 and the probability of the event.

Question 29

Two events A and B are independent if:

Accepted Answer

The occurrence of one event does not impact the probability of the other event.

Answer

The occurrence of one event makes the occurrence of the other event more likely.

Answer

The occurrence of one event makes the occurrence of the other event less likely.

Answer

The events cannot occur simultaneously.

Question 30

Bayes' theorem is used to:

Accepted Answer

Calculate the probability of a hypothesis being accurate given the evidence.

Answer

Calculate the probability of an event based on prior knowledge or assumptions.

Answer

Calculate the probability of two events occurring simultaneously.

Answer

Calculate the probability of an event not happening.

Question 31

Which of the following is a continuous probability distribution?

Accepted Answer

Normal distribution

Answer

Binomial distribution

Answer

Poisson distribution

Answer

Hypergeometric distribution

Question 32

The expected value of a random variable represents:

Accepted Answer

The average value of the random variable.

Answer

The most frequent value of the random variable.

Answer

The minimum value of the random variable.

Answer

The maximum value of the random variable.

Question 33

A random variable X has a mean of 5 and a standard deviation of 2. What is the probability that X takes a value between 3 and 7?

Accepted Answer

0.84

Answer

0.38

Answer

0.68

Answer

0.95

Question 34

Which of the following is a limitation of using Bayes' theorem?

Accepted Answer

It requires that the prior probabilities are known.

Answer

It can only be used to calculate the probability of one event.

Answer

It assumes that the sample space is finite.

Question 35

Which of the following is a key assumption in the use of probability distributions?

Accepted Answer

The sample size is large enough.

Answer

The outcome of an event is predictable.

Answer

The events are independent.

Answer

The probability of an event is constant over time.