random sampling

noun Statistics.
a method of selecting a sample (random sample) from a statistical population in such a way that every possible sample that could be selected has a predetermined probability of being selected.

Origin:
1895–1900

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Based on the Random House Dictionary, © Random House, Inc. 2014.
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WordNet
random sample

noun
1. a sample in which every element in the population has an equal chance of being selected 
2. a sample grabbed at random 
random sampling

noun
the selection of a random sample; each element of the population has an equal chance of been selected 
WordNet® 3.0, © 2006 by Princeton University.
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Example sentences
We intuitively know that facts gathered over time are a better random sample
  than any snapshot.
In other words, the pool of applicants for teaching and priesthood jobs are not
  a truly random sample.
But they don't, they take a random sample of whales of all sizes because that
  is what you do when you are doing research.
Those who took the test in its early phase were volunteers rather than a random
  sample of undergraduates.
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