Some Simple Propositions

Proposition 1
P(Ec) = 1 - P(E)
Proposition 2
, 則 .
Proof:
Since , it follows that we can express F as . Hence, as E and EcF are mutually exclusive, we obtain from Axiom 3 that P(F)=P(E)+P(EcF) which proves the result, since
Proposition 3

Proof:

Proposition 4

We may also calculate the probability that any one of the three events E or F or G occurs: which by Proposition 3 equals . Now it follows from the distributive law that the events and are equivalent, and hence we obtain from the preceding equations that