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data/knowledge_base/bayes_theorem.md
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# Bayes’ Theorem
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## Formula
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P(A | B) = [P(B | A) × P(A)] / P(B)
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## Total Probability
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If A₁, A₂, …, Aₙ are exhaustive events:
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P(B) = Σ P(B | Aᵢ)P(Aᵢ)
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## When to Use
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- Conditional probability
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- Inverse probability problems
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## Common Mistakes
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- Forgetting total probability
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- Confusing P(A|B) with P(B|A)
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