A probability between 0 and 1 does not guarantee a single result.
A likely outcome can fail to happen. Probability describes uncertainty, not a promise about one trial.
Show me why
A fair coin has a one-half probability of heads on a toss. That does not require heads on the next toss, or exactly five heads in ten tosses. Long-run regularity and an individual outcome are different ideas.
A common misconception
A run of tails does not make heads “due” on the next independent fair toss.
Where the limits are
This statement concerns non-certain events. Probabilities of 0 and 1 require care, especially in continuous models.
How we know
Under the relevant independence assumptions, the law of large numbers describes how relative frequencies approach probabilities over many trials. It does not prescribe a fixed sequence or require a streak to be corrected on the next trial.
What would change this conclusion?
This follows from the probability model. Evidence of bias or dependence changes which model applies.
Sources you can inspect
- OpenStax / Rice University3.1 Terminology — Statistics
Explains probability experiments and long-run frequency.
Publication date not stated · Checked in initial research 2026-10-08
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