Bayes’ Theorem

P (B_{i} | A) = \frac{P (A | B_{i}) \cdot P (B_{i})}{P (A)}

or

P (B_{i} | A) = \frac{P (A | B_{i}) \cdot P (B_{i})}{\sum_{i = 1}^{n} P (A | B_{i}) \cdot P (B_{i})}

or

P (B_{i} | A) = \frac{P (A | B_{i}) \cdot P (B_{i})}{P (A | B_{1}) \cdot P (B_{1}) + P (A | B_{2}) \cdot P (B_{2}) + . . . + P (A | B_{n}) \cdot P (B_{n})}

where

\sum_{i = 1}^{n} B_{i} = B_{1} + B_{2} + . . . + B_{n} = Ω

is a complete system of events.

In case i=1

P (B | A) = \frac{P (A | B) \cdot P (B)}{P (A)}; i = 1, B_{1} = B

Keywords:

Probability
Events, Operations with events, Complete system of events
Probability of an event
Conditional Probability
Law of Total Probability
Bayes’ Theorem
Discrete Probability Variable - Distribution Function
Statistics
Measures of Central Tendency
Statistics