Difference between revisions of "Bayes' Theorem"
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==Bayes' Theorem:== | ==Bayes' Theorem:== | ||
| − | Let <math>E_1</math> and <math>E_2</math> be two events, and <math>P(E_1 | E_2)</math> the probability of <math>E_1</math> dependent on <math>E_2.</math> Then <cmath>P(E_1 | E_2) = \dfrac{P(E_2 | E_1) \cdot P(E_1)}{P(E_2)}.</cmath> | + | Let <math>E_1</math> and <math>E_2</math> be two events, and <math>P(E_1 | E_2)</math> the [[probability]] of <math>E_1</math> dependent on <math>E_2.</math> Then <cmath>P(E_1 | E_2) = \dfrac{P(E_2 | E_1) \cdot P(E_1)}{P(E_2)}.</cmath> |
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Revision as of 10:45, 1 August 2022
Bayes' Theorem:
Let 
and 
be two events, and 
the probability of dependent on 
Then ![\[P(E_1 | E_2) = \dfrac{P(E_2 | E_1) \cdot P(E_1)}{P(E_2)}.\]](http://latex.artofproblemsolving.com/8/7/8/8788a644959ccf9f27057cf0f963e442c51bf3ff.png)
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