1.5 Discrete sample spaces Let E be an experiment with probability space (,F , P). The structure of this space depends greatly on whether  is a countable set (that is, a finite or countably infinite set) or an uncountable set. If  is a countable set, we normally take F to be the set of all subsets of , for the following reason. Suppose that  = {ω1,ω2, . . . } and, for each ω ∈ , we are interested