Randomness in statistics must be separated from the colloquial use of the word. In statistics, a random process – such as drawing names from a hat – requires that all possibilities have an equal chance of being selected.
A random sample requires that each possible sample of the same size from the population has the same chance of being selected. This creates a fair, unbiased sample and is essential if we are looking for a meaningful explanation for our data.
A single fair coin toss has a random outcome – but what happens when the toss is repeated many times?