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Random experiment
Definition
A random experiment is a process with an uncertain outcome drawn from a defined set of possible outcomes, called its sample space. It may be physical or abstract. Probability theory describes events and their probabilities within such a process. The term is broader than a randomized experiment used to estimate a causal effect.
What it means
Drawing a record at random, rolling a die or running a simulation with random inputs can each be modeled as a random experiment. The word experiment here does not require a laboratory intervention or a comparison of treatment groups. What matters is a clearly specified process and uncertainty about which outcome will occur. A probability model can make some outcomes more likely than others; random does not mean that every possible result has the same chance.
How it works
Specify the process, its sample space and the events of interest. Assign probabilities under a justified model, then define any random variables that summarize outcomes numerically. Repeated runs produce a sequence of outcomes, with independence or other dependence assumptions stated explicitly. The Aalto Dictionary of Machine Learning uses random experiments to explain probability spaces and data collection. Real repetitions may differ from idealized identical conditions, so the model should be checked against how the process actually operates. Long-run regularities require appropriate assumptions and do not determine the next individual result.
Three practical examples
- A hypothetical analyst samples one support ticket from a fixed collection and records its category, treating the selection as a random experiment.
- A machine-learning routine selects a minibatch according to a specified sampling rule; the selected records are the outcome of that random step.
- A simulation team draws uncertain arrival times to investigate queue behavior, distinguishing the assumed probability model from observed business demand.
Think of it this way
Think of drawing a labeled card from a well-defined deck. You know the possible cards and the drawing rule, but not which card will appear next. The analogy becomes misleading if the deck changes unnoticed, cards are not drawn as assumed or previous draws affect what remains. Those details determine the probability model.
Worked example
A box contains five blue tokens and three green tokens. One token is selected uniformly at random. The probability of blue is 5/8 and of green is 3/8. If the token is replaced and the box is remixed before a second independent draw, the probability of two blue outcomes is (5/8)² = 25/64. Without replacement, it is (5/8) × (4/7) = 5/14. The color counts are unchanged at the start, but the procedure changes the second-draw probabilities. This invented example shows why a random experiment must specify how repetition works rather than merely state that selection is random.
Illustrative case study
A fictional support-operations team wants to estimate how often tickets concern billing. It proposes selecting records randomly from a defined week's ticket collection. A review reveals that the export excludes tickets closed by an automated process, so the sampling frame does not represent all tickets. The team corrects the extraction and documents whether sampling is with or without replacement. It reports the sample-based estimate with uncertainty and avoids assuming the same rate applies to future weeks with different activity. The exercise shows that a sound random selection rule cannot compensate for an incorrectly defined population.
Common misconceptions and mistakes
A random experiment is not necessarily a randomized controlled trial. Random outcomes need not be equally likely, and repeated outcomes need not be independent. An event is a set of outcomes, while a random variable assigns a value to an outcome. A long sequence of one result does not automatically make the opposite result more likely on the next independent trial. Computer-generated pseudorandom values also come from an algorithm; reproducibility through a seed is compatible with using them to simulate a specified random process.
Business use
The concept supports sampling, simulation, testing and interpretation of uncertainty in AI workflows. Define the population or process before selecting a probability model. Record the sampling frame, replacement rule and dependencies that matter. When using simulation, distinguish variability generated by the model from uncertainty about whether the model itself is appropriate. Reproducible random seeds help compare computational runs, but multiple runs may be needed to assess variability. The business decision should reflect the actual data-generating process, not a convenient random mechanism assumed without evidence.
People also ask
Does random mean unpredictable in every respect?
The individual outcome is uncertain, while aggregate properties may be predictable under a suitable model.
Is a survey sample a random experiment?
A specified random sampling procedure can be modeled that way, though coverage and nonresponse still matter.
Does random assignment prove every causal assumption?
No. It helps with assignment comparability, but issues such as missing outcomes or interference can still require attention.
Check your understanding
Why do the token example's two-blue probabilities differ?
Answer: Removing the first token changes the composition for the second draw.
What is the sample space for two color draws?
Answer: The ordered color pairs blue-blue, blue-green, green-blue and green-green, with probabilities determined by the procedure.
Why does a random sample from an incomplete export remain limited?
Answer: It represents the exported records, not automatically the intended full population.
Related terms
- Sample space
- Event
- Random variable
- Probability distribution
- independent trials
- randomized experiment
Learn next
Write the sample space and events for a simple selection process. Then compare independent sampling, sampling without replacement and dependent sequences. Study the law of large numbers with its assumptions before interpreting repeated observations or simulated outcomes as inevitable patterns.
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Sources
Aalto Dictionary of Machine Learning, entries on random experiment, random variable and probability space: https://aaltodictionaryofml.github.io/ADictML_Main.pdf The token calculation and support-ticket case are original illustrations. The discussion distinguishes the supplied term's probability meaning from the narrower concept of a randomized causal experiment.
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