Bayes' rule with a simple and practical example

Bayes' theorem (alternatively Bayes' law or Bayes' rule) has been called the most powerful rule of probability and statistics. It describes the probability of an event, based on prior knowledge of conditions that might be related to the event. For example, if a disease is related to age, then, using Bayes' theorem, a person's age can be used to more accurately assess the probability that they have the disease, compared to the assessment of the probability of disease made without knowledge of the person's age. It is a powerful law of probability that brings in the concept of'subjectivity' or'the degree of belief' into the cold, hard statistical modeling. Bayes' rule is the only mechanism that can be used to gradually update the probability of an event as the evidence or data is gathered sequentially.