# Summary 2

Last updated: March 10th, 2020

# 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:

• $P(E')=1-P(E)$
• $P(E)=1-P(E')$