!!! Layman here so please avoid complex math and answers.
Random (usually pseudorandom) events are usually characterized along these lines:
- Each outcome in a trial experiment must be i.i.d.; i.e. it has no effect on subsequent outcomes, thus individual outcomes cannot be predicted using past data as there is no obvious causal link
- Large sequences of outcomes are predictable, because they exhibit a pattern of stabilizing relative frequencies, such that no individual outcome is "preferred" and dominates the rest
The prevailing thought in probability theory (frequentism) is that stabilizing relative frequencies are an objective phenomenon, independent of human thought. This assumption has served statisticians, casinos and insurance companies well. What this basically implies is that large sequences of similar random events are consistent and their averages can be confidently predicted within a "sufficiently" large sample.