Question 1

Which of the following best describes the Law of Large Numbers?

Accepted Answer

As the number of trials increases, the proportion of times a specific outcome occurs approaches a single value.

Question 2

A simulation is used to estimate probability. Which of the following best describes a simulation?

Accepted Answer

An imitation of chance behavior based on a model that accurately reflects the situation.

Question 3

Which of the following is the correct formula for the probability of the union of two events A and B?

Accepted Answer

$$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$

Question 4

If events A and B are mutually exclusive (disjoint), what is $$P(A \cap B)$$?

Accepted Answer

$$0$$

Question 5

Which of the following statements is TRUE about independent events?

Accepted Answer

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

Question 6

Given $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$P(A \cap B) = 0.2$$, what is $$P(A|B)$$?

Accepted Answer

$$0.2 / 0.5 = 0.4$$

Question 7

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

Accepted Answer

Probabilities can be negative if the event is unlikely.

Question 8

A random variable X is defined as the number of heads in three flips of a fair coin. What is the probability that X = 2?

Accepted Answer

$$\frac{3}{8}$$

Question 9

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

Accepted Answer

The number of defective light bulbs in a box.

Question 10

Which formula gives the mean (expected value) of a discrete random variable X with possible values $$x_i$$ and probabilities $$P(x_i)$$?

Accepted Answer

$$\mu_X = \sum x_i P(x_i)$$

Question 11

A binomial experiment has n = 5 trials and probability of success p = 0.4. What is the probability of exactly 2 successes?

Accepted Answer

$$\binom{5}{2} (0.4)^2$ (0.6)^3$

Question 12

Which condition must be met to use the normal approximation to the binomial distribution?

Accepted Answer

$$np \geq 10$$ and $$n(1-p) \geq 10$$

Question 13

If $$P(A) = 0.3$$ and $$P(B) = 0.5$$, and A and B are independent, what is $$P(A \cap B)$$?

Accepted Answer

$$0.15$$

Question 14

Which of the following phrases corresponds to the symbol $$\leq$$?

Accepted Answer

"no more than"

Question 15

A probability distribution for a discrete random variable must satisfy which two requirements?

Accepted Answer

Each probability is between 0 and 1, and the sum of all probabilities is 1.

Question 16

Which of the following is a correct interpretation of $$P(A^c)$$?

Accepted Answer

The probability that event A does not occur.

Question 17

Suppose you roll two fair six-sided dice. What is the size of the sample space?

Accepted Answer

36

Question 18

Which of the following is TRUE about mutually exclusive events?

Accepted Answer

They cannot occur together.

Question 19

If a random variable X has mean $$\mu_X$$ and variance $$\sigma_X^2$, what is the formula for the standard deviation?

Accepted Answer

$$\sigma_X = \sqrt{\sigma_X^2$}$$

Question 20

Which of the following is a key difference between discrete and continuous random variables?

Accepted Answer

Discrete random variables have countable values; continuous random variables have values in an interval.

Probability and Random Variables: Study Guide for Introductory Statistics

Study Guide - Practice Questions