(→In Multiple Events) |
(→In Multiple Events) |
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<math> \bigcap_i A_i = \prod_i P(A_i)</math> | <math> \bigcap_i A_i = \prod_i P(A_i)</math> | ||
| − | For i \in S | + | For i <math>\in</math> S |
==Conditional Probability== | ==Conditional Probability== | ||
Revision as of 10:15, 8 September 2008
Independence
In Two Events
$ P(A \bigcap B) = P(A) \times P(B) $
For example, given a coin, are the two outcomes independent?
$ P( \lbrace C_1=H \rbrace \bigcap \lbrace C_2 =H \rbrace ) $
In Multiple Events
$ \bigcap_i A_i = \prod_i P(A_i) $
For i $ \in $ S
Conditional Probability
A & B are conditionally independent given C if the following formula holds true.
$ P(A \bigcap B|C) = P(A|C) \times P(B|C) $
