Background
Probability Theory
Pascal's Triangle & Probability
Application of Probability Theory
Pascal's wager
Objections
Homework
Joyce Lam Nga Ching
2001714828
Phil1007
12-4-2002
27-4-2002
Probability
Theory
Glossary of Probability Terms
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.
Go to Gambling On God
Reference:
