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.

{\displaystyle P(A\mid B)={\frac {P(A\cap B)}{P(B)}},}

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.

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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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