| Line 2: | Line 2: | ||
<MATH> P(A)=P(A|C)P(C)+P(A|C^c)P(C^c) </MATH> | <MATH> P(A)=P(A|C)P(C)+P(A|C^c)P(C^c) </MATH> | ||
| + | |||
| + | |||
<MATH>P(A|B)=P(A|B \bigcap C)P(C|B)+P(A|B \bigcap C^c)P(C^c|B) </MATH> | <MATH>P(A|B)=P(A|B \bigcap C)P(C|B)+P(A|B \bigcap C^c)P(C^c|B) </MATH> | ||
| + | |||
| + | <MATH>P(A|B \bigcap C)P(C \bigcap B)/P(B) </MATH> | ||
Revision as of 20:07, 15 September 2008
The theorem of total probalility states that
$ P(A)=P(A|C)P(C)+P(A|C^c)P(C^c) $
$ P(A|B)=P(A|B \bigcap C)P(C|B)+P(A|B \bigcap C^c)P(C^c|B) $
$ P(A|B \bigcap C)P(C \bigcap B)/P(B) $
