Yasmin Youssef – Ph.D. studies 2022 Cairo University Faculty of Economics and Political Science Socio-Computing Department Bayes Theorem and real-life applications Abstract: Bayes' theorem is an important part of inference statistics and many advanced machine learning models. Bayesian inference is a logical approach to updating the potential of hypotheses in the light of new knowledge, and therefore naturally plays a central role in science. It explains the likelihood of an event based on prior knowledge of circumstances that may be relevant to the event. Bayes' theorem provides a method of calculating the degree of uncertainty. (Berrar, 2018). It can be applied in our daily lives when we are attempting to make a decision based on new information. The aim of this research is to shed light on the various fields in which this theory is applied. Keywords: Bayes’ Theorem, Probability, Total Probability, Conditional Probability. Introduction The Bayes Theorem is a statistical and probability-based mathematical paradigm that seeks to compute the likelihood of one situation based on its relationship with another scenario. It is the single most important rule for good decision-making. Bayes theorem uses the available information and incorporates “conditional probabilities” into conclusions. It can produce posterior probability distributions that are biased by prior probabilities. Bayes' Theorem has made significant progress in history. During World War II, the theorem was employed to crack the famed Nazi Enigma encryption. The translations taken from the Enigma encryption machine used to crack the German message code were assessed using Bayes Theorem by Alan Turing, a British mathematician. Turing and his team deciphered the German Enigma code by using probability models to break down the nearly unlimited number of possible translations of the messages that were most likely to be translated. (McNamara, Green, & Olsson, 2006) Bayes Theorem Formula The most popular and pervasive formula used for Bayes' Theorem is as follows: P(A ∣ B) = P(B ∣ A)P(A) / P(B)