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Naive Bayes classifiers makes the naive assumption that the features are independent. They make use of Bayes theorem.

Naive Bayes classifiers make use of Bayes theorem:

$$\overbrace{P(c | X)}^{\text{A posteriori}} = \frac{\overbrace{P(X | c)}^{\text{Likelihood}} \cdot \overbrace{P(c)}^{\text{A priori} } }{\underbrace{P(X)}_{\text{evidence}}}$$

See also