- The
**complement**of an event contains all outcomes that are not in . The**union**{ or } of events and contains all outcomes in , in , and in both and . The**intersection**{ and } contains all outcomes that are in both and , but not outcomes in alone or alone. - The
**conditional probability**of an event , given an event , is defined by

when . In practice, conditional probabilities are most often found from directly available information.206

- The essential general rules of elementary probability are
**Legitimate values:**for any event**Total probability 1:****Complement rule:****Addition rule:****Multiplication rule:**

- If and are
**disjoint,**then . The general addition rule for unions then becomes the special addition rule, . - and are
**independent**when . The multiplication rule for intersections then becomes . - In problems with several stages, draw a
**tree diagram**to organize use of the multiplication and addition rules. - If are disjoint events whose probabilities are not 0 and add to exactly 1 and if is any other event whose probability is not 0 or 1, then
**Bayes's rule**can be used to calculate as follows: