# Events and sample space

My book said that a sample space is the set of all possible outcomes of a random experiment and that events are groups of outcomes of the sample space. After it said that an impossible event is the empty set.

Thus events can be or subsets of the sample space, or the whole sample space, or the empty set?

Thank you so much for your time.

• Events are subspaces of the sample space. – steven gregory Jan 24 '18 at 17:13

Yes -- an event is a subset of the sample space. For any set $S$, $\varnothing$ and $S$ are both subsets of $S$, so the characterization in the previous sentence includes the empty set and the whole space.