# Definition

A probability distribution on a countable Sample space $\Omega$ is a Function $$\mathbb{P}: \Omega \to [0,1]$$ such that $$\sum_{\omega \in \Omega} \mathbb{P}(\omega) = 1$$.

# Intuition

We express a belief that “$x\in \Omega$ happens with probability $$r$$” by setting $$\mathbb{P}(x) = r$$. So a probability distribution divides up our anticipation of what will happen, out of the set $$\Omega$$ of things that might possibly happen.

examples, futher points

Parents:

• Probability theory

The logic of science; coherence relations on quantitative degrees of belief.