**Basic Axioms of Probability**:

(a)
for any set *A*.

(b)
,
where
is the sample space.

(c) If
is a sequence of mutually
exclusive events, that is for all *i* and *j* different:
we have the finite additivity property:

Consequences:

Property 1:

Property 2:

Property 3:

Special Case:
**If ***E*** and ***F*** are disjoint, (mutally exclusive)**,
then:

Property 4:

If

Definition:

We define a partition of the sample
space
to be a sequence of pairwise disjoint sets
whose union is .
Property 5:

If
forms a partition
of
then:

Property 6:

Property 7: