Total Probability Rule

The total probability rule explains an unconditional probability of an event, in terms of that event's conditional probabilities in a series of mutually exclusive, exhaustive scenarios.

Probability of event A is:

P(A) = P(AlS) P(S) + P(AlS^C) P(S^C)
where: S is one of the scenario and S^C is complement of scenario S

P(A) = P(AlS1) P(S1) + P(AlS2) P(S2)… + P(AlSn) P(Sn)
where: S1, S2, … , Sn are mutually exclusive and exhaustive events.