Difference between revisions of "Geometric probability"
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| + | ==Geometric Counting and Probability== | ||
| + | https://youtu.be/OOdK-nOzaII?t=1858 | ||
| + | |||
== Introduction == | == Introduction == | ||
| − | When dealing with a [[probability]] problem involving [[discrete]] quantities, we often times just use the fact that | + | When dealing with a [[probability]] problem involving [[discrete]] quantities, we often times just use the fact that probability is the ratio of the number of successful outcomes to the number of total outcomes. |
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. | 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 == | ||
| − | + | * [https://artofproblemsolving.com/wiki/index.php/1998_AIME_Problems/Problem_9 AIME 1998/9] | |
| − | * [ | + | * [https://artofproblemsolving.com/wiki/index.php/2004_AIME_I_Problems/Problem_10 AIME 2004I/10] |
| + | * [https://artofproblemsolving.com/wiki/index.php/2015_AMC_10A_Problems/Problem_25 2015 AMC 10A Problem 25] | ||
| + | [[Category:Combinatorics]] | ||
| + | [[Category:Definition]] | ||
| + | [[Category:Geometry]] | ||
Revision as of 22:50, 18 November 2023
Geometric Counting and Probability
https://youtu.be/OOdK-nOzaII?t=1858
Introduction
When dealing with a probability problem involving discrete quantities, we often times just use the fact that probability is the ratio of the number of successful outcomes to the number of total outcomes.
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.
