SECTION 4.3 Summary

• 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.

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• 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: