Multiplication Rule of Probability || Lesson 35 || Probability & Statistics || Learning Monkey ||

Multiplication Rule of Probability
In this class, We discuss the Multiplication Rule of Probability.
The reader should have prior knowledge of independent events. Click Here.
Multiplication Rule:
In a random experiment, if A, B are two events such that P(A) != 0 and P(B) != 0 then P(A ∩ B) = P(A) P(B | A).
P(B ∩ A) = P(B) P(A | B)
Proof:
From conditional probability P(A | B) = P(A ∩ B)/P(B)
P(A ∩ B) = P(B) P(A | B)
Similarly, P(B | A) = P(B ∩ A)/P(A)
P(B ∩ A) = P(B | A) P(A)
For Dependent Events:
P(A ∩ B) = P(B) P(A | B)
For Independent Events:
P(A ∩ B) = P(B) P(A | B) Where P(A | B) = P(A) for independent events.
P(A ∩ B) = P(B) P(A)

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