Probability space
Once the probability space is established, one usually assumes that “nature” makes its move and selects a single outcome, ω, from the sample space Ω. All the events in  that contain the selected outcome ω (recall that each event is a subset of Ω) are said to “have occurred”. The selection performed by nature is done in such a way that if the experiment were to be repeated an infinite number of times, then the relative frequencies of occurrence of each of the events would coincide with the probabilities described by the function P.