Multiplication Rule of Probability

In this class, We discuss the Multiplication Rule of Probability.

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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)