Probability Help and Tutorials by Topic

What Is Probability?
This is an explanation of some of the basics of probability.

How to Use a Tree Diagram
Tree diagrams are helpful to compute the probabilities of several independent events. See the steps involved in making and using a tree diagram for tossing two coins.

Multiplication Rule
What happens to the probabilities of two independent events?

Independent
A defintion of independent events in probability.

Elementary Probability Tutorials
This site has several tutorials dealing with basic concepts in probability.

What Is the Factorial?
The factorial gives us a way to compactly write the product of several consecutive positive whole numbers. Find values and learn problem solving skills with the factorial.

Combinations and Permutations
Combinations and permutations are both used in probability, but they are easy to get confused. Find out the difference between these two closely related ideas in combinatorics.

Probabilities of Rolling Two Dice
It is straightforward to calculate the probabilities for rolling one die. Things can get a little dicey when there are two or more. Find out how to calculate the probabilities for rolling two dice.

What Is the Expected Value
The expected value is a measure of the center of a probability distribution.

When Do You Use a Binomial Distribution
It can be hard to know when a binomial distribution is appropriate. Check out what conditions are needed before you start using this kind of a probability distribution.

Mutually Exclusive
The concept of being mutually exclusive is an idea from probability. To calculate some compound probabilities, we must know whether the component events are mutually exclusive or not.

What Are Probability Axioms?
The foundations of probability are based upon three axioms. Other formulas and theorems pertaining to probability can be logically deduced from these beginning three statements.

Uniform in Probability
One common assumption in basic probability problems is that the sample space being used is uniform. This describes what is meant by a uniform probability distribution.

What Is the Intersection?
The set theory operation of intersection looks at two sets and tells us those things that are in common with both.

What Is the Union?
One common operation that can be performed on two sets is the union. This is a way of grouping the elements from two sets into one new set.

What Is the Difference of Two Sets?
Subtraction is typically thought of as a process involving two numbers. This notion of a difference can be generalized to the realm of set theory.

Probabilities for Rolling Three Dice
Finding probabilities for rolling three dice extends the ideas needed to calculate the probabilities associated to rolling two dice.

What Is the Barber Paradox?
Russell's barber paradox shows what kinds of problems can arise when we are not careful with our definitions. The traditional definition of a set was turned on end by Russell's paradox.

What Is Set Theory?
Set theory forms the foundation for much of mathematics. The areas of probability is particular is based upon basic ideas concerning sets.

What Is Markov's Inequality?
Markov's inequality is a result from probability, that like Chebyshev's inequality, is a general result applying to a wide variety of distributions.

How Are Odds Related to Probability?
Probability and odds both describe the likelihood of an event. But these two topics look at this in a slightly different ways. Probability compares the number of successes to the total number of attempts, whereas the the odds in favor of an event compares the number of successes to the number of failures.

What Is a Probability Distribution?
A probability distribution is a function or rule that assigns probabilities to a random variable. This can be done in a list, a table or even a graph.

Why Does Zero Factorial Equal One?
The factorial is a shorthand way to write multiplication of several numbers. Also in the definition is the fact that 0! = 1. Find out why this is true.

Chebyshev's Inequality
Chebyshev's inequality is a mathematical theorem that states that at least a certain amount of data must fall within a stated number of standard deviations from the mean.

What Is the Prisoner's Dilemma?
The prisoner's dilemma is an example of a game where the rational choice is to choose an outcome that is not the most beneficial. It has been studied as an example of a non-zero sum game and has wide applications to other areas.

What Is the Empty Set?
The empty set is a feature of set theory that can seem somewhat strange. It is an example of where nothing can become something.

What is the Probability of Rolling a Yahtzee?
Yahtzee is a dice game in which one of the goals is to obtain five matching dice during a possible three rolls. This is difficult to do, but not impossible. Find out what's the probability of rolling a Yahtzee.

Sampling With or Without Replacement
Sampling can be done in several different ways. We can either replace the objects that we sample, or not replace them.

What Is the Gamma Function?
The gamma function shows up throughout statistics and probability. This function generalizes the factorial for values other than positive whole numbers.

What Is Conditional Probability?
For conditional probability we are calculating the probability of an event, based upon the fact that another event has already occurred.

Probability and Monopoly
Monopoly is a board game that involves the rolling of a pair of dice. We can use this probabilistic feature of the game to calculate the probabilities of landing on certain spaces during the first two turns of the game.

What Is a Sample Space?
A sample space is an important concept in probability. This topic is concerned with all of the possible outcomes of a probability experiment.

What Is a Standard Deck of Cards?
A standard deck of cards is a widely used example in basic probability. Learn about the important features for this popular sample space.

What Is the Birthday Problem?
The birthday problem, also known as the birthday paradox, asks what the probability is that there is at least one shared birthday in a group of people. Find out how to solve this problem in probability.

What Is an Event
In probability set theory can be used to define probability and do calculations. One important set is called an event. The event is a subset of the sample space.

Using Conditional Probability to Compute Probability of Intersection
The formula for conditional probability can be rewritten to calculate the probability of the intersection of two events. This version of the formula gives us a good way to determine if two events are independent.

What Is the Probability of a Flush
A flush is a hand in poker that has five cards of the same suit. Discover how unlikely this is to occur.

Expected Value in Roulette
The game of roulette is a good example of the application of expected value. We can analyze what the winnings will be in the long run if we continually bet on red.

Probability of Going to Jail in Monopoly
The board game Monopoly features a space known as jail. What is the probability that on your turn you will end up going to jail?

Expected Value of a Binomial Distribution
The binomial distribution shows up in a variety of applications of discrete random variables. The expected value is a measurement of the center of the distribution and can be calculated in a relatively straightforward way.

What Is the Importance of the Central Limit Theorem?
The Central Limit Theorem is an important result from probability. One question that comes up is what makes this theorem so important to the practical uses of statistics?