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)