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! colspan="2" style="background: #eee;" | Property of Probability Functions
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| align="right" style="padding-right: 1em;" | The complement of an event A (i.e. the event A not occurring) || <math>\,P(A^c) = 1 - P(A)\,</math>
 
| align="right" style="padding-right: 1em;" | The complement of an event A (i.e. the event A not occurring) || <math>\,P(A^c) = 1 - P(A)\,</math>

Revision as of 09:36, 22 October 2010

Properties 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 }. $

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