The figure below shows the results of two different sets of...

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Key Concepts

Short-Term Variability

In a small sample of coin tosses, random fluctuations can lead to noticeable deviations from the expected probability. These variations are natural and can result in outcomes that seem uneven or patterned, but they do not imply a bias in the coin or the process of tossing.

Long-Term Stability

Over many trials, the effects of random variation diminish, and outcomes tend to stabilize around their theoretical probabilities. This means that in long sequences of coin tosses, even if early results appear anomalous, the overall distribution of results will eventually closely reflect the expected statistical probabilities.

Law of Large Numbers

This principle explains that while outcomes of random events may vary widely in the short run, the average of the results will converge to the expected value as the number of trials increases. In coin tosses, while short-term sequences might show streaks or imbalances, with a large number of tosses, the proportion of heads and tails will tend to approximate a 50/50 split.

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