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Which distribution fits the question?
Start with what one observation means, then describe how it is generated. The chooser suggests lessons and makes the remaining assumptions explicit. It does not fit a distribution to your data.
Choose an answer to continue. “I do not know” is a useful answer: it identifies what to investigate next.
Try three different questions
- Heads in ten independent flips of the same coin: choose a count, fixed trials, and independent trials with the same probability. This gives a binomial count, even when p is unknown.
- Draws of one color from a bag without replacement: choose a count and fixed trials, then uniform sampling from a known finite collection. This gives hypergeometric rather than binomial.
- Uncertainty about the coin’s p after seeing flips: choose a probability, then uncertainty about a shared Bernoulli parameter. Beta is a candidate prior; the observed flips themselves are Bernoulli.
What a match establishes
A mechanism can imply a distribution mathematically. Applying it to observations still requires checking whether that mechanism is a useful description. Bounds, exposure, dependence, changing probabilities, and the measurement process matter. Similar-looking histograms may hide very different tail probabilities.
For a direct numerical comparison, see Poisson vs binomial and normal vs Student t. For definitions, return to reading distributions or explore the learning paths.
Reference
NIST’s distribution gallery documents many of the families linked here. The chooser is an educational guide to their stated assumptions, not a statistical model-selection test.