The sample space |\boldsymbol{(\Omega)}| is the set of all possible outcomes of a random experiment.
To list the elements in the sample set, simply enumerate all the possible outcomes inside braces. The sample set is represented by the Greek letter Omega |(\Omega).|
We want to write out all the possible outcomes when we roll a |6|-sided die.||\Omega = \{1, 2, 3, 4, 5, 6\}||
If the experiment has more than one step, we list, in brackets, the different possible results at each step, in the form of pairs, triples, etc.
We want to enumerate all the possible outcomes (sample space) when a |4|-sided die is rolled |2| times.||\begin{align} \Omega = \big\{&(1,1), (1,2), (1,3), (1,4),\\ &(2,1), (2,2), (2,3), (2,4),\\ &(3,1), (3,2), (3,3), (3,4),\\ &(4,1), (4,2), (4,3), (4,4)\big\} \end{align}||
We want to enumerate all the possible outcomes when a coin is flipped |3| times in a row.
||\begin{align} \Omega = \big\{&(T,T,T), (T,T,H), (T,H,T), (T,H,H),\\ &(H,T,T), (H,T,H), (H,H,T), (H,H,H)\big\} \end{align}||
It’s possible to use different modes of representation, such as the tree diagram or the Venn diagram, to help enumerate the possible outcomes.