Law of Total probability

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PAS

Cegep/2

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53 words

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1 minute

Suppose event $A$ and partitions $B_{1}, B_{2}, \dots B_{k}$ , then

P (A) = \sum_{i = 1}^{k} P (A \cap B_{i}) = \sum_{i = 1}^{k} P (B_{i}) P (A | B_{i})

[!abstract] Partition
Each of the pairwise disjoint events $E$ such that $E_{1} \cup E_{2} \cup \dots E_{k} = Ω$

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