Randomness is the lack of pattern or predictability in events.

A random sequence of events, symbols or steps has no order and does not follow an intelligible pattern or combination.

The notion of randomness:

The sequences satisfying the definition of randomness form a set of probability one with respect to the measure that makes all coordinates independently take the values 0 and 1 with probability ½.

A recursive sequence is necessarily non-random. A simple random sample is chosen in such a way that every set of individuals has an equal chance to be in the selected sample.