Axioms/Postulates of Probability

We can use some postulates or axioms to define this probability. Axioms or postulates are forms of basic assumptions that we make to characterize anything that are logically coherent and non-overlapping. Typically, such postulates are derived by considering feasible features that we would like to see in the defined thing. There is no way to prove or disprove these fundamental assumptions. The probability or chance of occurrence of the event A will be defined by the following three postulates.

The Postulates

(i) 0 ≤ P(A) ≤ 1 or the probability of an event is a number between 0 and 1, both inclusive;

(ii) P(S) = 1 or the probability of the sure event is 1;

(iii) P(A1 ∪ A2 ∪ ⋯) = P(A1) + P(A2) + ⋯ whenever A1,A2,... are mutually exclusive [The events may be finite or countably infinite in number]

The characteristic 0≤P(A)≤1 corresponds to the requirement that a relative frequency be between 0 and 1. The fact that an outcome from the sample space happens on every trial of an experiment results in the property P(S) = 1.

On this topic, your comments/suggestions are highly appreciated.

SEE YOU IN THE NEXT TOPIC:

>INTRODUCTION to PROBABILITY

>AREAS UNDER THE NORMAL CURVE