Bayes' theorem
![A blue neon sign, showing the simple statement of Bayes' theorem](/Images/godic/202412/23/Bayes'_Theorem_MMB_015500.jpg")
![Visualization of Bayes' theorem by the superposition of two decision trees](/Images/godic/202412/23/Bayes'_Theorem_2D.svg5500.png")
![Tree diagram illustrating drug testing example. U, Ū,](/Images/godic/202412/23/Bayes_theorem_drugs_example_tree.svg5500.png")
![A geometric visualisation of Bayes' theorem. In the table, the values w, x, y and z give the relative weights of each corresponding condition and case. The figures denote the cells of the table involved in each metric, the probability being the fraction of each figure that is shaded. This shows that P (A |B ) P (B ) = P (B |A ) P (A ) i.e. P (A |B ) = P (B |A ) P (A )/P (B ) . Similar reasoning can be used to show that P (Ā|B ) = P (B |Ā) P (Ā)/P (B ) and so forth.](/Images/godic/202412/23/Bayes_theorem_visualisation.svg5501.png")
In probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule) describes the probability of an event, based on conditions that might be related to the event. For example, suppose one is interested in whether a person has cancer, and knows the person's age. If cancer is related to age, then, using Bayes' theorem, information about the person's age can be used to more accurately assess the probability that they have cancer.