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3,249 notes

3,249 notes

Multiplication Theorem · cho.sh

Multiplication Theorem

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In Probability,

$P (\cap_{k=1}^{n} A_k) = P(A_1) P(A_2 | A_1) \cdots P(A_n | A_1 \cap A_2 \cdots A_{n-1})$

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k

)

=

P(A1)P(A2∣A1)⋯P(An∣A1∩

A2⋯An−1)

if independent

$P (\cap_{k=1}^{n} A_k) = \prod\limits_{k=1}^n (A_k)$

$P(A|B) = {P(A \cap B) \over P(B)} {=^{\text{ind}}} P(A)$

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