Just trying to get my head around writing out the technical definitions of sample space and events in terms of sets, given a situation.
Consider the following example.
There are two urns. Urn 1 contains 2 white and 3 blue balls. Urn 2 contains 3 white and 4 blue balls. A ball is drawn randomly from Urn 1 and placed into Urn 2. Then a ball is picked at random from Urn 2 and examined. We are interested in the probability of this ball being blue.
Let $B$ be the event the ball taken from Urn 1 is blue.
I am trying to write out what $\Omega$, $\mathcal{F}$ and $B$ would be in terms of sets.
My guess is that
$$ \begin{align*} \Omega&=\{(b,b),(b,w),(w,b),(w,w)\}\\ \mathcal{F}&=\{0,1\}^\Omega\\ B&=\{(b,b),(b,w)\} \end{align*} $$
Are these the most natural definitions?