Many of the methods used for dealing with uncertainty in expert systems are based on Bayes' Theorem.

Notation:

P(A) | Probability of event A |

P(A B) | Probability of events A and B occurring together |

P(A | B) | Conditional probability of event A |

given that event B has occurred | |

If *A* and *B* are * independent*, then *P(A | B) = P(A)*.

Expert systems usually deal with events that are * not* independent,
e.g. a disease and its symptoms are not independent.

Bayes' Theorem

*P (A B) = P(A | B)* P(B) = P(B | A) * P(A)*
therefore *P(A | B) = P(B | A) * P(A) / P(B)*