Bayes' Theorem formula, also known as Bayes' Law, or Bayes' Rule, is an intuitive idea. We adjust our perspective (the probability set) given new, relevant information. Formally, Bayes' Theorem helps us move from an unconditional probability (what are the odds the economy will grow?) to a conditional probability (given new evidence, what are the odds the economy will grow?)
Suppose your daughter tells you that her friend is coming home tomorrow. Since you don't know anything else, there is a 50% chance that the friend is a female. Now she tells you that her friend has long hair. With this additional information there are now more chances that the friend is a female. Bayes' theorem can be applied in such scenarios to calculate the probability (probability that the friend is a female.)
A simple representation of Bayes' formula is as follows:
- P(A) is the initial degree of belief in A (probability of A).
- P(A/B) is the degree of belief after having accounted for B.
- P(B/A)/P(B) represents the support provided by B to A.
The following video provides a good overview of how Bayes' Theorem works.