Probability Review I

Notions of Probability

Let us look at two notions of the probability of an event happening:

The Frequentist Version

Given $N$ distinct possible events, $\left(x_{1},x_{2},\ldots ,x_{N}\right)$, with the following assumptions:

• No two events can occur simultaneously, and
• The events occur with frequencies $\left(n_{1},n_{2},\ldots ,n_{N}\right)$,

Then the probability of an event $x_{i}$ is given by:

$P\left(x_{i}\right)={\frac {n_{i}}{\sum _{j=1}^{N}n_{j}}}$

(1)

From this definition, we can see that:

$\sum _{j=1}^{N}P\left(x_{i}\right)=1$

(2)