TOTAL PROBABILITY THEOREM
![]()
- The Total Probability Theorem allows you to get the probability of an event without conditioning from the probabilities of that same event when it is conditioned.
- Note that
- So
Which is known as the "Total Probability Lemma."
The more general Total Probability Theorem states: This can be viewed pictorially as
where the total probability of being in state Y=y depends on the sum of the probabilities of beginning in each state and transitioning from (multiplication) each When all the ways of ending in state Y=y have been accounted for, then that is the total probability.
![]()
RELATED
CONCEPTSConditional Probability Bayes Theorem ![]()
Copyright © 1998 Rensselaer Polytechnic Institute. All Rights Reserved.