Typically, when the sample space is finite, any subset of the sample space is an event (that is, all elements of the power set of the sample space are defined as events). However, this approach does not work well in cases where the sample space is uncountably infinite. So, when defining a probability space it is possible, and often necessary, to exclude certain subsets of the sample space from being events (see § Events in probability spaces, below).
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Event (probability) in the context of Coincidence
A coincidence is a remarkable concurrence of events or circumstances that have no apparent causal connection with one another. The perception of remarkable coincidences may lead to supernatural, occult, or paranormal claims, or it may lead to belief in fatalism, which is a doctrine that events will happen in the exact manner of a predetermined plan. In general, the perception of coincidence, for lack of more sophisticated explanations, can serve as a link to folk psychology and philosophy.
From a statistical perspective, coincidences are inevitable and often less remarkable than they may appear intuitively. Usually, coincidences are chance events with underestimated probability. An example is the birthday problem, which shows that the probability of two persons having the same birthday already exceeds 50% in a group of only 23 persons. Generalizations of the birthday problem are a key tool used for mathematically modelling coincidences.
View the full Wikipedia page for Coincidence