Probablity theory, sigma-algebra, rolling two dices and having partial information about outcome.

Question

I was looking at this example to understand sigma-algebra better and why they are a good tool for probabilities.
So my basic understanding about sigma-fields, is that the set in them are the events, so we can say after the "probability experiment" whether this event/set is realized or not. In the linked question, the experiment is as follows :
We throw 2 dices and the information we get back is wether we had two sixes, one six or no sixes. So I guess that the sample space can be $\Omega=\{1,...,6\}\times \{1,...,6 \}.$
At some point they say that the sigma-algebra should be the power set $2^\Omega$.
But is this true? If I consider $A=\{(1,6)\} \in 2^\Omega$, with the information I have at the end of the experiment I can't say whether this event is realized with the information at hand, no? So A wouldn't be an event, i.e. it shouldn't be in the sigma-algebra, no?