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How do repeated coin tosses demonstrate the relative-frequency interpretation of probability?

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sample space for a pair of dice — probability theory Sample space for a pair of dice.

In probability theory, the relative-frequency interpretation posits that the probability of an event is the ratio of its occurrences to the total number of trials as that number becomes very large. Repeated coin tosses serve as a classic demonstration of this concept.12

While the outcome of any single toss is unpredictable, the collective results of many trials display regularity. According to the relative-frequency interpretation, stating that the probability of "heads" is one-half implies that in a large number of tosses, the frequency of heads will be approximately 50 percent.1

This relationship is formally supported by the law of large numbers, which proves that as the number of independent trials increases, the sample mean (the fraction of heads) approaches the theoretical probability. It is important to note that this convergence does not rely on a "mystical force" to correct short-term deviations; rather, as the number of tosses grows, any initial imbalance becomes statistically insignificant relative to the total number of trials.3