Definition: RulesOfProbabilty

Definition: Rules (or Axioms) of Probability

• If \(S\) is the samples space, \(P(S) = 1\).
• For any event \(A\), \(0 \leq P(A) \leq 1\).
• If \(A\) and \(B\) are mutually exclusive events, \(P(A \text{ or } B) = P(A) + P(B)\).
  • If \(A^c\) is the complement of \(A\), then \(P(A^c) = 1 - P(A)\).

If two events \(A\) and \(B\) do not share any outcomes, \(P(A \text{ and } B) = 0\), then they are mutually exclusive events (the events cannot occur at the same time).

Source: These definitions are taken from OpenStax Introductory Statistics and Statistics for Engineers and Scientists by Navidi.