Given 
mutually exclusive events 
, ..., 
whose probabilities sum to unity, then
 |
where 
is an arbitrary event, and 
is the conditional
probability of 
assuming 
.
Total Probability Theorem
See also
Bayes' Theorem, Conditional Probability, Inclusion-Exclusion Principle, Mutually Exclusive EventsExplore with Wolfram|Alpha
References
Papoulis, A. Probability, Random Variables, and Stochastic Processes, 2nd ed. New York: McGraw-Hill, pp. 37-38, 1984.Referenced on Wolfram|Alpha
Total Probability TheoremCite this as:
Weisstein, Eric W. "Total Probability Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TotalProbabilityTheorem.html