This chapter summarizes the rules you have been using for adding and multiplying probabilities, and for using conditional probability. It also gives a pictorial way to understand the rules.
The rules that follow are informal versions of standard axioms for elementary probability theory.
ASSUMPTIONS
The rules stated here take some things for granted:
▪ The rules are for finite groups of propositions (or events).
▪ If A and B are propositions (or events), then so are AvB, A&B, and ∼A.
▪ Elementary deductive logic (or elementary set theory) is taken for granted.
▪ If A and B are logically equivalent, then Pr(A) = Pr(B). [Or, in set theory, if A and B are events which are provably the same sets of events, Pr(A) = Pr(B).]
NORMALITY
The probability of any proposition or event A lies between 0 and 1.
1. (1) 0 ≤ Pr(A) ≤ 1
Why the name “normality”? A measure is said to be normalized if it is put on a scale between 0 and 1.
CERTAINTY
An event that is sure to happen has probability 1. A proposition that is certainly true has probability 1.
(2) Pr(certain proposition) = 1
Pr(sure event) = 1
Often the Greek letter Ω is used to represent certainty: Pr(Ω) = 1.
ADDITIVITY
If two events or propositions A and B are mutually exclusive (disjoint, incompatible), the probability that one or the other happens (or is true) is the sum of their probabilities.
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