TOTAL PROBABILITY THEOREM [brown line]


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."

[brown line] 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.

[brown line]

RELATED
CONCEPTS

Conditional Probability
Bayes Theorem
[brown line]

Copyright © 1998 Rensselaer Polytechnic Institute. All Rights Reserved.