Law of Total Probability

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

or

P (A) = 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.

Keywords: Law of Total Probability

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