Probability Learning Quizzes for Master of Education (MEd) Students

Question 1

Which of the following properties is true for probability?

Accepted Answer

It ranges from 0 to 1.

Accepted Answer

It adds up to 1 for mutually exclusive events.

Answer

It can be negative.

Question 2

Which of the following is NOT a property of probability?

Accepted Answer

Probabilities can be negative.

Answer

Probabilities must be between 0 and 1.

Answer

The sum of probabilities of all possible outcomes equals 1.

Answer

Probabilities can be estimated using data.

Question 3

Which probability distribution is used to model the number of successes in a sequence of independent trials?

Accepted Answer

Binomial distribution

Answer

Poisson distribution

Answer

Normal distribution

Answer

Exponential distribution

Question 4

A bag contains 4 white balls and 6 black balls. If two balls are drawn without replacement, what is the probability of drawing a white ball and then a black ball?

Accepted Answer

2/15

Answer

1/5

Answer

1/3

Answer

2/5

Question 5

What event is complementary to the event of rolling a 6 on a six-sided die?

Accepted Answer

Rolling a number less than 6

Answer

Rolling a 1

Answer

Rolling a 2

Answer

Rolling a number greater than 6

Question 6

Which of the following describes the Bayesian approach to probability?

Accepted Answer

Updating probabilities based on new information

Answer

Using frequentist data to make inferences

Answer

Focusing solely on objective probability

Answer

Ignoring prior knowledge

Question 7

How many possible outcomes exist when rolling two fair dice?

Accepted Answer

36

Answer

6

Answer

12

Answer

24

Question 8

Which of these variables is a continuous random variable?

Accepted Answer

A person's height

Answer

Number of students in a classroom

Answer

Score on a test

Answer

Number of weekdays in a week

Question 9

Which of these methods is effective for teaching probability?

Accepted Answer

Incorporating real-world examples and simulations

Answer

Solely focusing on theoretical concepts

Answer

Emphasizing rote memorization

Answer

Disregarding technology

Question 10

What is the formula for calculating the probability of an event, where n(E) represents the number of favorable outcomes and n(S) represents the total number of possible outcomes?

Accepted Answer

P(E) = n(E) / n(S)

Answer

P(E) = n(E) * n(S)

Answer

P(E) = n(S) / n(E)

Answer

P(E) = n(E) + n(S)

Question 11

Which of the following is a feature of a continuous probability distribution? It:

Accepted Answer

Can take on any value within a specified range.

Answer

Is represented by a discrete graph.

Answer

Has a finite number of possible outcomes.

Answer

Can only take on integer values.

Question 12

The mean of a binomial distribution, where n represents the number of independent trials and p represents the probability of success, is:

Accepted Answer

np

Answer

np(1-p)

Answer

np(1+p)

Answer

np^2

Question 13

Which of the following is NOT an assumption of the Poisson distribution? It assumes that:

Accepted Answer

The distribution is continuous.

Answer

Events occur independently of each other.

Answer

The average number of events per unit is constant.

Answer

The probability of two events occurring simultaneously is negligible.

Question 14

The expected value of a random variable X with probability mass function P(X = x) is calculated as:

Accepted Answer

E(X) = Σx * P(X = x)

Answer

E(X) = √x * P(X = x)

Answer

E(X) = ∫x * P(X = x) dx

Answer

E(X) = x * P(X = x)

Question 15

In Bayesian inference, the prior probability represents:

Accepted Answer

Our initial beliefs about a parameter before observing data.

Answer

The distribution of the data.

Answer

The posterior probability.

Answer

The statistical model.

Question 16

In a fair coin toss, heads are assigned a value of 1 and tails a value of 0. What is the expected value of the toss?

Accepted Answer

0.5

Answer

0.25

Answer

1

Answer

0

Question 17

What is the variance of a binomial distribution with n = 10 and p = 0.4?

Accepted Answer

2.4

Answer

1.6

Answer

8

Answer

4

Question 18

Which of the following is a fundamental axiom of probability?

Accepted Answer

The probability of an event cannot exceed 1.

Answer

The probability of an event is always greater than or equal to the probability of its complement.

Answer

The sum of the probabilities of all possible outcomes must be equal to 0.

Question 19

What is Bayes' theorem primarily used for?

Accepted Answer

Determining the probability of an event based on prior knowledge or conditional events.

Answer

Testing the significance of differences between two groups.

Question 20

A population has a mean of 100 and a variance of 25. A sample of 36 observations is randomly selected from this population. What is the standard error of the mean?

Accepted Answer

2.5

Answer

5

Answer

10

Answer

25

Question 21

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

Accepted Answer

3/8

Answer

1/4

Answer

1/2

Answer

1/16

Question 22

A fair coin is flipped five times. What is the expected number of heads in these five flips?

Accepted Answer

2.5

Answer

3

Answer

4

Answer

2

Question 23

A company manufactures light bulbs with a mean lifespan of 1000 hours and a standard deviation of 50 hours. Assuming the lifespan follows a normal distribution, what is the approximate probability that a randomly chosen light bulb will last less than 950 hours?

Accepted Answer

0.0228

Answer

0.8413

Answer

0.9772

Answer

0.1587

Question 24

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

Accepted Answer

The sum of all probabilities must be greater than 1.

Answer

All possible outcomes must be mutually exclusive.

Answer

The probability of each event must be between 0 and 1.

Answer

The sum of all probabilities must be equal to 1.