7. Probability axioms#
The discussion about what probability is, as well as the interpretation of what it means, has been going on for centuries, and we won’t cover it here. Lukcily, most modern perspectives on probability are compatible and can be traced back to a few key fundamental concepts, known as the axioms of probability. These three axioms are summarized here:
The probability of any event is \([0,1]\).
The set of all possible outomes has probability 1.0.
If two events are mutually exclusive, the probability of both events (the union) is the sum of their probabilities: \(P[A \cup B]=P(A)+P(B)\)
While they may seem simple, these axioms are actually precise mathematical statements that provide the basis for a number of theorems and proofs which allow us to apply probability theory to a wide range of applications.