Hey Developer’s, I’m back with a new topic which is Multiplicative and Additive Law Of Probability in the series of statistics foundations.
Quick Refresher
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.
So, let’s get started …
Multiplicative Law Of Probability
As we learned before the formula of conditional probability,
P(A|B) = P(A∩B) / P(B)
The probability of intersection of two events A and B is
P(A∩B) = P(B)P(A|B) = P(A)P(B|A),if values swapped
If these events are independent, then P(A∩B) = P(A)P(B)
Multiplicative Law Examples
Two Dependent Events:
- A – Odd Number
- B – number < 4
P(A) = 1/2 ; P(B) = 1/2
P(A|B) = 2/3; P(B|A) = 2/3
Explanation: Only two odd numbers out of nmber < 4 means 3 values {1,2,3}. so 2/3.
P(A∩B) = P(A)P(B|A) = 1/2 * 2/3 = 1/3
Additive Law Of Probability
Probability of a union of events, P(A U B) = P(A) + P(B) – P(A∩B)
If A and B are mutually exclusive,P(A∩B) = 0 and
P(A U B) = P(A) + P(B)
We can extend this formula to calculate the probabilities of more than 2 events.
Next Post will be on Laws Of Total Probability
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