Application of Theorem of Total Probability
It is used for the evaluation of the denominator in Bayes’ theorem. Bayes’ Theorem for n set of events is defined as,
Let E1, E2,…, En be a set of events associated with the sample space S, in which all the events E1, E2,…, En have a non-zero probability of occurrence. All the events E1, E2,…, E form a partition of S. Let A be an event from space S for which we have to find probability, then according to Bayes’ theorem,
P(Ei|A) = P(Ei)P(A|Ei) / ∑ P(Ek)P(A|Ek)
for k = 1, 2, 3, …., n
Mathematics – Law of Total Probability
The law of total probability is important to find the probability of an event happening. If the probability of an event is going to happen is known to be 1, then for an impossible event it is likely to be 0. A fundamental rule in the theory of probability that is interconnected to marginal probability and conditional probability is called the law of total probability, or the total probability theorem.
After several events, it is known that the probability of all the possibilities should be known. The theorem of total probability is the core foundation of Baye’s theorem. In this article, we have discussed important concepts related to total probability, including the law of total probability, statements, proofs, and some examples.