Bayes' theorem

Etymology
Named after English mathematician (1701–1761), who developed an early formulation. The modern expression of the theorem is due to, who extended Bayes's work but was apparently unaware of it.

Proper noun

 * 1)  A theorem expressed as an equation that describes the conditional probability of an event or state given prior knowledge of another event.

Usage notes
The theorem is stated mathematically as:
 * $$\displaystyle P(A\mid B) = \frac{P(B \mid A) \, P(A)}{P(B)}$$,

where $$\textstyle A$$ and $$\textstyle B$$ are events with $$\textstyle P(B)\neq 0$$, and
 * $$\textstyle P(A)$$ and $$\textstyle P(B)$$ are the of observing $$\textstyle A$$ and $$\textstyle B$$ without regard to each other.
 * The $$\textstyle P(A\mid B)$$ is the probability of observing event $$\textstyle A$$ given that $$\textstyle B$$ is true.
 * Similarly, $$\textstyle P(B\mid A)$$ is the probability of observing event $$\textstyle B$$ given that $$\textstyle A$$ is true.