# Axioms of Probability

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## Definition: Axioms of Probability

Axioms are propositions that are not susceptible of proof or disproof, derived from logic.

There are three axioms of Probability which are as under:

First Axiom of Probability

It states that the probability of any event is always a non-negative real number, i.e., either 0 or a positive real number. It cannot be negative or infinite. The smallest possible number is 0. The set of real number here includes both rational and irrational number.

However, it doesn’t put any upper limit on the value of probability of an event ( which can maximum be one as we know!)

Second Axiom of Probability

It states that the probability of all the events, i.e., the probability of the entire sample space is 1.

Mathematically, if S represents the Sample space, then P(S)=1.

This means that there are no events outside the sample space and it includes all possible events in it.

Third Axiom of Probability

Two events which don’t have anything in common, i.e., which don’t intersect are called mutually exclusive.

This axiom states that for two event A and B which are mutually exclusive,

P (A U B) = P(A)+ P(B)

Similarly, extending the result to n mutually exclusive events X1, X2, X3, X4 and so on,

P(X1 U X2 U X3 U X4 U ......)= P(X1) + P(X2) + P(X3) + P(X4) +.......

Hence, this concludes the definition of Axioms of Probability along with its overview.

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