Difference between revisions of "Probability"
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* [[dependent probability]] | * [[dependent probability]] | ||
* [[independent probability]] | * [[independent probability]] | ||
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| + | == Formal Definition of Probability == | ||
| + | Probability is formally defined as a triple <math>(\Omega, \mathfrak{a}, \mathit{P})</math>. Here <math>\Omega</math> is a set called the sample space, <math>\mathfrak{a}</math> is a class of events from the sample space, and <math>\mathit{P}:\mathfrak{a}\to [0,1]</math> is an assignment with certain properties called the probability function. | ||
=== Types of Probability === | === Types of Probability === | ||
Revision as of 08:01, 27 November 2007
Probability is one of the most difficult areas of mathematics to define, explain, or understand. Probability can be loosely defined as the chance that an event will happen.
Contents
Introductory Probability
Before reading about the following topics, a student learning about probability should learn about introductory counting techniques.
Formal Definition of Probability
Probability is formally defined as a triple 
. Here 
is a set called the sample space, 
is a class of events from the sample space, and ![$\mathit{P}:\mathfrak{a}\to [0,1]$](http://latex.artofproblemsolving.com/b/2/7/b27773111c820ad61d748abdece0c1822e1a1c69.png)
is an assignment with certain properties called the probability function.
Types of Probability
Part of a comprehensive understanding of basic probability includes an understanding of the differences between different kinds of probability problems.
- algebraic probability
- combinatorial probability problems involve counting outcomes.
- geometric probability
