### Probability Axioms

In this post we will look into probability axioms there are 3 basic axioms of probability and it is mentioned below

**Axiom 1 : For any set A**

**Axiom 2 : **

**Axiom 3 : if A_1, A_2, ... is any set of disjoint events, then**

**Definition **

if A = \bigcup\limits_{i=1}^{\infty} A_i,. and A_1, A_2, .... are disjoint, then A_1, A_2, .... is said to be a partition of A

Axiom 3 also holds for finite collection of events A_1,..., A_n which is trivially true if you set A_{n+1} = \emptyset for all i \in \N

By using the above axioms we can get more axioms. Below are the results from axioms

**Compliments**

**Differences**

if A is contained in B ( A \subset B), then

P(B \cap A^c) = P(B) - P(A)**Inclusion – Exclusion**

### Equally likely outcomes

In some cases, we can safely assume the outcomes are equally likely like if we roll a fair dice or toss a fair coin twice or more.

Suppose

- n_A is the number of sample points in event A
- N is the number of sample points in a finite sample space \Omega

if all outcomes are equally likely in a sample space \Omega, then the probability that event A occurs is

P(A)=\frac{n_A}{N},- n_A is the number of sample points in A
- N is the number of sample points in \Omega

So in this post we have seen the Axioms of probability and in the next post we will start with Counting

Happy Learning

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