====== Probability ======
The observation made on a system $S$ can lead to many outcomes. What is the probability of an outcome $X$? To answer this, we have to imagine an **ensemble** $\Sigma$ of systems similar to $S$. Then the probability of of the outcome $X$

$$ P(X) = \lim_{N(\Sigma)\rightarrow \infty} \frac{N(X)}{N(\Sigma)} $$

where $N(\Sigma)$ is the total number of systems in the ensemble $\Sigma$ and $N(X)$ is the number of systems exhibiting the outcome $X$.

$P(X)$ is a number from $0$ to $1$.