2.8 BASIC PROBABILITY RESULTS
The following propositions follow from the three axioms of probability. They also illustrate how to rearrange a problem statement in terms of disjoint sets for which one can use Axiom 3 to derive the result.
Proposition 2.2. .
Proof. Since and :
(2.45)
which gives and .
Proposition 2.3. For event , P(Ec) = 1−P(E).
Proof. Since and :
(2.46)
which can be rewritten as P(Ec) = 1−P(E).
Proposition 2.4. If , then .
Proof. Since F contains E, it can be partitioned in ...
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