A probability sample is one in which each member of the population has the same probability of being included. An alternative and equivalent definition is that it is a sample such that the probability of selecting that particular sample is the same for all samples of that size which could be drawn from the population.
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Not sure about the "best" definition. It is the set of all possible outcomes for the event.
Set of all possible outcomes.
Since there is only one definition given, it has to be better than the ones which are not even featured!
In a probability sample, each unit has the same probability of being included in the sample. Equivalently, given a sample size, each sample of that size from the population has the same probability of being selected. This is not true for non-probability sampling.
There are two equivalent ways of defining a simple random sample from a larger population. One definition is that every member of the population has the same probability of being included in the sample. The second is that, if you generate all possible samples of the given size from the population, then each such sample has the same probability of being selected for use.