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Definition of the conditional probability
of *A* given *B*:

Averaging rule:

*P*(*E*)=*P*(*E*|*F*)*P*(*F*)+*P*(*E*|*F*^{c})*P*(*F*^{c})

General Averaging Rule:

Let
be a
partition
of ,
by which I mean that the events
*F*_{i} are all mutually exclusive and that their union is ,
then:

Bayes Rule:(how to find the opposite conditional
probability than the ones given):

General Bayes Rule:

Let
be a
partition
of ,
then
is a partition of *E* and:

*Susan Holmes*

*1998-12-07*