Mutually exclusive events

Definition

Two events, \(A\) and \(B\) are called mutually exclusive if they have no outcomes in common. More precisely, using set notation, this is when

\[ A \cap B = \emptyset \]

In other words, \(A\) and \(B\) are called mutually exclusive if they cannot occur at the same time.

Properties of probability

In 1933, Kolmogorov published a paper basing the 'theory' of probability to a small number of axioms that hold for all definitions of probability. Anything derived from these axioms also holds, no matter how probability is defined, so we no longer need to distinguish between the different definitions in the last section.

Axioms of probability

  1. P(S) = 1       where S is the sample space
  2. 0 ≤ P(E) ≤ 1        for any event, E
  3. P(A or B) = P(A) + P(B)         if events A and B are mutually exclusive

These axioms are central to probability. The rest of probability theory can be derived from them.