These are the axioms of [[Comparative Probability]], which were formalized by the Mathematician [[Alexey Kolmogorov]] in 1933. An alternative approach to formalising [[Probability]], favoured by some [[Bayesians]], is given by [[Cox's theorem]]. The assumptions as to setting up the axioms can be summarised as follows: Let $(\Omega, F, P)$ be a [[Measure Space]] with $P(E)$ being the [[Probability]] of some [[Event]] `E`, and $P(\Omega)=1$. Then $(\Omega, F, P)$ is a [[probability space]], with sample space $\Omega$, event space $F$ and [[probability measure]] $P$. The axioms are the following. 1. All events have a [[real number]] probability of at least 0. $\forall E \in F$, $P(E) \in \mathbb{R}$ and $P(E) \ge 0$ 2. $P(\Omega) = 1$ 3. For [[mutually exclusive]] events, the probability of any of them happening is the same as the sum of the probabilities of the individual events.