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Multiplication Rule of Probability

Multiplication Rule of Probability

Nov 11, 20251 min read

statistics
probability
math

Rule

P (A_{1} \cap \dots \cap A_{n}) = P (A_{1}) \times P (A_{2} ∣ A_{1}) \times P (A_{3} ∣ A_{2}, A_{1}) \times \dots P (A_{n} ∣ A_{n - 1}, \dots, A_{1})

Works with any order

Mutual Events Rule

For mutual events $A_{1}, \dots, A_{n}$ Then, $P (A_{1} \cap \dots \cap A_{n}) = P (A_{1}) \times \dots \times P (A_{n})$

Usage in Conditional Probability

$P (A \cap B ∣ C) = P (A ∣ B, C) P (B ∣ C)$

Graph View

Rule
Mutual Events Rule
Usage in Conditional Probability

Backlinks

Conditional Probability Density Function
Probability Theory

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