Difference between revisions of "Geometric probability"
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| − | ''' | + | == Introduction == |
| + | When dealing with a [[probability]] problem involving [[discrete]] quantities, we often times just use the fact that <math>\text{Probability}=\frac{\text{Number of successful outcomes}}{\text{Number of total outcomes}}</math>. | ||
| + | |||
| + | However, we can have a situation where the quantities are [[continuous]]. We can still use the same notion that probability is the ratio of successful outcomes to total outcomes, but we cannot simply count the number of successful outcomes and the number of total outcomes. Instead, we have to find the size of each set. This is where we turn to '''geometric probability'''. We can usually translate a probability problem into a [[geometry]] problem. We can use [[length]] for one dimension, [[area]] for two dimensions, or [[volume]] for three dimensions. | ||
== Examples == | == Examples == | ||
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=292973#p292973 AIME 2004I/10] | * [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=292973#p292973 AIME 2004I/10] | ||
Revision as of 11:23, 22 June 2006
Introduction
When dealing with a probability problem involving discrete quantities, we often times just use the fact that 
.
However, we can have a situation where the quantities are continuous. We can still use the same notion that probability is the ratio of successful outcomes to total outcomes, but we cannot simply count the number of successful outcomes and the number of total outcomes. Instead, we have to find the size of each set. This is where we turn to geometric probability. We can usually translate a probability problem into a geometry problem. We can use length for one dimension, area for two dimensions, or volume for three dimensions.
