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:
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: