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Glossary of Probability Terms

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

Bernoulli Trial: Another name for a trial in a binomial experiment.

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

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.

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

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

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

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

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

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.

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

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.

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.

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

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

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

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

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

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

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

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

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

Fairness of a Game: A game is considered fair if its expected value equals 0.

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

Fundamental Counting Principle: A method used to calculate all of the possible combinations of a given number of events.

Heuristics: Strategies that people use to solve problems.

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

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

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

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.

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

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

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

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

Mutually Exclusive Events: Events that cannot occur at the same time.

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).

Outcome: A result of an experiment.

Percent: A ratio of a number to 100.

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

Probability: The likelihood that an event will occur.

Probability Distribution: The set of probabilities associated with the values in a random variable’s sample space.

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

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).

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

Sample Size: The number of trials in an experiment.

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

Standard Deviation: Measures how the elements in a set vary from the set’s mean.

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

Theoretical Probability: Probability of an outcome occurring based on probability principles.

Tree Diagram: A method of visualizing and listing an experiment’s sample space.

Trial: A single repetition of an experiment.

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


References

     Borwein, J., Watters, C., & Borowski, E.  (1997).  Interactive Math Dictionary [Computer Software].  Halifax, Nova Scotia, Canada: MathResource, Inc.  (1.0).

     Brown, R. G.  (1997).  Advanced Mathematics.  Evanston, IL: McDougal Littell, Inc.

     Collins, W., Cuevas, G., Foster, A.G., Gordon, B., Moore-Harris, B., Rath, J., Swart, D., & Winters, L.J.  (1998).  Algebra I.  New York: Glencoe.

     Dolciani, M.P., Beckenbach, E.F., Donnelly, A.J., Jurgensen, R.C., & Wooton, W.  (1980).  Modern Introductory Analysis.  Boston: Houghton Mifflin. 

     Dolciani, M.P., Sorgenfrey, R.H., Graham, J.A., & Myers, D.L.  (1988).  Introductory Analysis.  Boston: Houghton Mifflin.

     Gerver, Sgroi, Carter, Hansen, Molina, & Westegaard.  (1997).  Algebra 2 Mathematics Handbook.  Cincinnati: Southwestern.