Axiomatic approach to probability:

Axiomatic approach to probability:

Axioms  is a statement or proposition that is regarded as being established, accepted, or self-evidently true. The modern approach to probability is purely axiomatic and it is based on the set theory. The axiomatic approach to probability was introduced by the Russian mathematician A.N.  Kolmogorov in the year 1933.

Axioms of probability: 

Let S be a sample space and A be an event in S and P(A) is the probability satisfying the following axioms:

(1)               The probability of any event ranges from zero to one.

i.e        0 ≤ P(A) ≤ 1

(2)               The probability of the entire space is 1.

i.e P(S) = 1

(3)               If A1, A2,… is a sequence of mutually exclusive events in S, then P (A1 È A2 È …) = P(A1) + P(A2) +...

Interpretation of statistical statements in terms of set theory: 

S          Þ Sample space

A         Þ A does not occur A È A =  S

A Ç B = f Þ A and B are mutually exclusive.

A È B Þ Event A occurs or B occurs or both A and B occur. (at least one of the events A or B occurs)

A Ç B Þ Both the events A and B occur. A Ç B Þ Neither A nor B occurs

A Ç B Þ Event A occurs and B does not occur A Ç B Þ Event A does not occur and B occur.