# Summary 2¶

In this section we started by defining what an experiment with **equally likely results** is: an experiment in which *every outcome* have the *same chances of occur*.

Then from the fact that *all the probabilities add up to $1$* we deduced that:

#### If $\Omega$ has equally likely results and $|\Omega|=n$, then $P(\omega)=\dfrac{1}{n}$ $\forall\omega\in\Omega$.¶

Now thinking in terms of *events* we noticed that:

#### If $\Omega$ has equally likely results, and $E\subseteq\Omega$, then $P(E)=\dfrac{|E|}{|\Omega|}$.¶

After that we learnt to use *Venn Diagrams* and *Combinatorics* to find probabilities of experiments with *equally likely results*.

We also thought about experiments *without equally likely results* and reached the conclusion that in those cases the probability was going to be calculated as a **proportion**.

This means, $P(E)=\dfrac{successful \ cases}{total \ amount \ of \ cases}$.

In the end, we exploited the fact that $P(E)+P(E')=1$ to find *two useful formulas*:

- $P(E')=1-P(E)$
- $P(E)=1-P(E')$