Problem with not independent events I have the following problem which I'm not sure how to solve:
Let $\Omega=\{A,B,C\}$ be the sample space of events happening on some experiment and $P(A)=\frac{1}{2}, P(B)=\frac{1}{3}$. Find the probabilities of all random events related with this experiment.
My understanding is that I have to find all subsets of $\Omega$, but I'm not sure how to do that since the events might be dependent on each other.
I try $P(A\cup B)=P(A)+P(B)-P(A\cap B)$ but I don't know whether $P(A\cap B)=P(A)P(B)$.
Another approach I try is:
$P(\overline A)=P((B\cup C) \setminus A)=\frac{1}{2}$
$P(\overline B)=P((A\cup C) \setminus B)=\frac{2}{3}$,
but I don't think this takes me anywhere too.
Is there a missing condition in the statement of the problem for independence of the events, or is there a way to solve the problem which I'm missing.
Thanks in advance!

$A,B,C$ aren't events. They're sample points. 

Events are subsets of the sample space.

By definition, for a finite sample space, the probability of an event is the sum of the probabilities of the sample points which are elements of the event.

Also, for a finite (or countable) sample space, the sum of the probabilities of all the sample points must be $1$, so $C$ has probability $1/6$.

Since the sample space has $3$ elements, it has$\;2^3=8\;$subsets. Thus, there are$\;8\;$events. For each event, write it in set notation (for example, $\{A,B\}$), and find its probability by summing the probabilities of its sample points.
