Title: 35_4 Total Probability and Bayes’ Theorem
Course: HELM Workbooks 2023-2024 > Section: HELM 35: Sets and Probability

When the ideas of probability are applied to science and engineering (and many other areas) there are occasions when we need to calculate conditional probabilities other than those already known. For example, if production runs of ball bearings involve say, four machines, we might know the probability that any given machine produces faulty ball bearings. If we are inspecting the total output prior to distribution to users, we might need to know the probability that a faulty ball bearing came from a particular machine. Even though we do not address the area of statistics known as Bayesian Statistics here, it is worth noting that Bayes’ theorem is the basis of this branch of the subject.