← Apply probability concepts

8 Comparing true, model, and experimental probability

A recurring Excellence part gives you multiple estimates of the same quantity — a stated true/national figure, a model or theoretical value, and an experimental (sampled) value — and asks which is most reliable, and why.

The three sources, and when each is trustworthy

  • True/national probability: calculated from a complete census or the entire population — the most reliable, when genuinely available.
  • Model/theoretical probability: derived from an assumed structure (e.g. "each digit equally likely") — only as good as the assumption behind it.
  • Experimental probability: observed relative frequency from an actual sample — subject to sampling variation, especially with a small sample size.
  • A large, well-designed experimental sample can be MORE reliable than a theoretical model built on a shaky assumption — reliability is not simply a fixed ranking of the three types.
Exam-style Ranking three probability estimates for reliability For cricket participation: the true 2023 census value is 8,880/50,000; a random sample of 1,000 finds 120 played cricket; a coordinators' model estimates 25%. Which is most reliable for predicting future participation? The TRUE census value (8,880/50,000 = 17.76%) is the most reliable estimate of what actually happened in 2023, since it covers the whole population, not a sample. The EXPERIMENTAL sample (120/1,000 = 12%) is subject to sampling variation — a different sample of 1,000 could easily give a different result, so it is less certain than the census figure. The MODEL estimate (25%) may be based on outdated assumptions or an unrepresentative coordinators' judgement, and is the LEAST anchored to actual current data of the three. For PREDICTING FUTURE participation specifically, note that even the true 2023 census value is now historical — the real question is which figure best represents likely future conditions, not just which was most reliable in 2023. ✓ A full-credit answer ranks the three AND explains the reasoning behind each ranking, rather than just asserting an order. ✕

Assuming true probability is always available and always wins

A "true" population probability is only available when a genuine census exists — many real exam scenarios only give you a model estimate and an experimental sample, with no true value stated at all. Do not invent a ranking that assumes a true value exists when the resource does not actually provide one.

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