 We may now apply the theory to various familiar cases. For example, we may represent the results of tossing a single die once by the set \(\Omega = \{1, 2, 3, 4, 5, 6\}\), and we could let \(\mathbf{F}\) be the set of all subsets of \(\Omega\). Under the natural assignment of probabilities to members of \(\mathbf{F}\), we obtain such welcome results as the following: 