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| − | ! colspan="2" style="background: #e4bc7e; font-size: | + | ! colspan="2" style="background: #e4bc7e; font-size: 120%;" | |
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! colspan="2" style="background: #eee;" | Property of Probability Functions | ! colspan="2" style="background: #eee;" | Property of Probability Functions | ||
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| align="right" style="padding-right: 1em;" | Event A occurs given that event B has occurred || <math>\,P(A \mid B) = \frac{P(A \cap B)}{P(B)}\,</math> | | align="right" style="padding-right: 1em;" | Event A occurs given that event B has occurred || <math>\,P(A \mid B) = \frac{P(A \cap B)}{P(B)}\,</math> | ||
| + | |- | ||
| + | | align="right" style="padding-right: 1em;" | Total Probability Law || <math>\,P(B) = P(B|A_1)P(A_1) + \dots + P(B|A_n)P(A_n)\,</math> | ||
| + | <math> \mbox{ where } \{A_1,\dots,A_n\} \mbox{ is a partition of sample space } S, B \mbox{ is an event }.</math> | ||
| + | |- | ||
| + | | align="right" style="padding-right: 1em;" | Bayes Theorem || <math>\,P(A_j|B) = \frac{P(B|A_j)P(A_j)}{\sum_{i=1}^{n}P(B|A_i)P(A_i)},\ \{A_i\} \mbox{ and } B \mbox{ are as above }.</math> | ||
|} | |} | ||
---- | ---- | ||
[[Collective_Table_of_Formulas|Back to Collective Table]] | [[Collective_Table_of_Formulas|Back to Collective Table]] | ||
[[Category:Formulas]] | [[Category:Formulas]] | ||
Revision as of 08:35, 22 October 2010
| Property of Probability Functions | |
|---|---|
| The complement of an event A (i.e. the event A not occurring) | $ \,P(A^c) = 1 - P(A)\, $ |
| The intersection of two independent events A and B | $ \,P(A \mbox{ and }B) = P(A \cap B) = P(A) P(B)\, $ |
| The union of two events A and B (i.e. either A or B occurring) | $ \,P(A \mbox{ or } B) = P(A) + P(B) - P(A \mbox{ and } B)\, $ |
| The union of two mutually exclusive events A and B | $ \,P(A \mbox{ or } B) = P(A \cup B)= P(A) + P(B)\, $ |
| Event A occurs given that event B has occurred | $ \,P(A \mid B) = \frac{P(A \cap B)}{P(B)}\, $ |
| Total Probability Law | $ \,P(B) = P(B|A_1)P(A_1) + \dots + P(B|A_n)P(A_n)\, $
$ \mbox{ where } \{A_1,\dots,A_n\} \mbox{ is a partition of sample space } S, B \mbox{ is an event }. $
|
| Bayes Theorem | $ \,P(A_j|B) = \frac{P(B|A_j)P(A_j)}{\sum_{i=1}^{n}P(B|A_i)P(A_i)},\ \{A_i\} \mbox{ and } B \mbox{ are as above }. $ |
