Hey Developer’s, I’m back with a new topic which is Independence Of Events in the series of statistics foundations.

### Quick Refresher

**Conditional probability is defined as the likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome.**

**Unconditional Probability is defined as the likelihood that an event will take place independent of whether any other events take place or any other conditions are present.**

So, let’s get started …

### Independence of Events

**Two events A and B are independent if events do not influence one another**.

If any of the following condition holds, then the two events A and B are independent,

- P(A|B) = P(A)
- P(B|A) = P(B)
- P(A∩B) = P(A)P(B)

If none of these condition holds, the events are **dependent** and if any one of the condition holds from this the events are **independent**.

### How to calculate the independence of events?

**Example:**

**Consider these events generated by a single die roll:**

- A: odd number rolled
- B: even number rolled
- C = {1,2}

**Are A and B independent ?**

- First calculate, P(A)=1/2, P(B) = 1/2 because in a die roll there are 50% chances of odd and 50% chances of even numbers. Even ={2,4,6},Odd = {1,3,5}. Total = 6 possibilities. P(Even or A) = 3/6 = 1/2 and P(Odd or B) = 3/6 = 1/2.
- Since, A∩B = ∅ and P(A/B)=0 because at the same time a die roll cannot be an even and an odd number.
- P(A|B)
*≠*P(A), so events are**dependent**

**Are A and C independent ?**

- P(A|C) = 1/2, P(A) =1/2, P(C)=2/6 = 1/3 , P(A∩C) = P(A)*P(C) = 1/6
- P(A|C) = P(A∩C)/P(C) = (1/6)/(1/3) = 1/2
- P(A) = 1/2
- P(A|C) = 1/2 = P(A)
- Events are
**independent**

#### Next Post will be on Multiplicative and Additive Law Of Probability

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