Probability

Independent Events

Events in which the outcome of one event does not affect the outcome of the other event.

Mutually Exclusive Events

Events that cannot occur at the same time.

Dependent Events

Events in which the outcome of one event affects the outcome of the other event.

Random Variable

"A function that assigns a numerical value to each outcome of an experiment" (Dolciani, 1988). "The outcomes form the sample space of the Random Variable" (Dolciani, Beckenbach, Donnelly, Jurgensen, & Wooton, 1980).

Odds

"A ratio obtained either from the number of ways the events can occur and could fail to occur, or from the probabilities of the complementary events" (Gerver, Sgrui, Carter, Hansen, Molina, & Westegaard, 1997).

Matrix

"A rectangular arrangement of elements in rows and columns" (Collins, 1998).

Binomial Distribution

"A statistical distribution giving the probability of obtaining a specific number of successes in a binomial experiment" (Borwein, Watters, & Borowski, 1997).

Event

"A subset of a sample space" (Brown, 1997).

Simple Event

"An event that contains a single outcome" (Dolciani, 1988). Also called an Elementary Event.

Elementary Event

"An event that contains a single outcome" (Dolciani, Sorgenfrey, Graham, & Myers, 1988). Also called a Simple Event.

Equally Likely Outcomes

"Outcomes that have an equal chance of occurring" (Collins, Cuevas, Foster, Gordon, Moore-Harris, Rath, Swart, & Winters, 1998).

Sample Space

"The set of all possible outcomes of an experiment" (Dolciani, 1988).

Fairness of a Game

A game is considered fair if its expected value equals 0.

Permutation

A group of elements from a set in which the order of the elements is important.

Combination

A group of elements from a set in which the order of the elements is not important.

Tree Diagram

A method of visualizing and listing an experiment's sample space.

Fundamental Counting Principle

A method used to calculate all of the possible combinations of a given number of events.

Percent

A ratio of a number to 100.

Outcome

A result of an experiment.

Trial

A single repetition of an experiment.

Experiment

An action that has various outcomes that occur unpredictably and can be repeated indefinitely under the same conditions.

Random Event

An event that cannot be predicted with certainty and that is chosen without any preference over other events.

Impossible Event

An event that cannot occur; it has a probability of 0.

Compound Event

An event that consists of two, or more, simple events; for example: A or B; A and B and C.

Certain Event

An event that must occur; it has a probability of 1.

Binomial Experiment

An experiment that has a fixed number of independent trials; each trial has 2 possible outcomes (success and failure) and the probability for success is the same for each trial.

Bernoulli Trial

Another name for a trial in a binomial experiment.

Law of Large Numbers

If the number of trials of an experiment is large, then the outcomes' experimental probabilities will be close to the outcomes' theoretical probabilities.

Frequency

Measures how often something occurs within some given distance or time period.

Standard Deviation

Measures how the elements in a set vary from the set's mean.

Empirical Probability

Probability estimate for an outcome of an experiment based on the outcome's empirical frequency; also called Experimental Probability.

Experimental Probability

Probability estimate for an outcome of an experiment based on the outcome's experimental frequency; also called Empirical Probability.

Theoretical Probability

Probability of an outcome occurring based on probability principles.

Disjoint Sets

Sets that do not have any of the same elements; their intersection is an example of an empty set or a null set.

Heuristics

Strategies that people use to solve problems.

Expected Value

The average value an experiment is expected to produce if it is repeated a large number of times.

Mode

The element in a set of numbers that occurs the most often in the set.

Compound Probability

The likelihood that a compound event will occur; for example: P(A or B); P(A and B and C).

Conditional Probability

The likelihood that an event will occur given that another event has already occurred; for example: P(A|B) = P(A) given that B has already occurred.

Probability

The likelihood that an event will occur.

Median

The middle element in a set of numbers that are in numerical order.

Experimental Frequency

The number of times an outcome has been observed to occur during repeated trials of an experiment; also called Empirical Frequency.

Empirical Frequency

The number of times an outcome has been observed to occur during repeated trials of an experiment; also called Experimental Frequency.

Theoretical Frequency

The number of times an outcome is expected to occur during repeated trials of an experiment based on probability principles.

Sample Size

The number of trials in an experiment.

Complementary Probabilities

The probability of an outcome occurring and the probability that the same outcome will not occur.

Probability Distribution

The set of probabilities associated with the values in a random variable's sample space.

Union of sets

The set that contains any element that belongs to one, or more, of the original sets.

Intersection of sets

The set that contains only the elements that belong to each of the original sets.

Mean

The sum of a set of elements divided by the number of elements in the set; also called Average or Weighted Average.

Average

The sum of a set of elements divided by the number of elements in the set; also called the Mean or Weighted Average.

Deviation

The sum of the absolute values of the differences between the theoretical outcomes and the experimental outcomes of events divided by the number of events. This is used to statistically compare experimental results with theoretical results.

Complementary Events

Two events from the same sample space whose probabilities add up to 1.