How does relative frequency explain the probability of heads in many coin tosses?

In probability theory, the relative frequency interpretation provides a way to understand the probability of an event, such as tossing "heads" on a coin, through the observation of repeated trials.1

Relative Frequency and Probability

The relative frequency of an event is defined as the ratio of the number of times that specific event occurs to the total number of trials conducted. When applied to coin tossing, the statement that the probability of heads is one-half implies that, in a large number of tosses, the relative frequency of heads will be approximately one-half. This interpretation does not predict the outcome of any single toss but describes the regularity observed across a collective series of trials.21

The Law of Large Numbers

The relationship between relative frequency and theoretical probability is formalized by the law of large numbers. This theorem states that as the number of independent, identically distributed trials increases, the observed sample mean (the relative frequency of heads) approaches the theoretical probability (1/2).3

It is important to note that this convergence occurs over the long term; the law does not require any "mystical force" to correct short-term deviations, as it may take a significant number of tosses for the relative frequency to stabilize near the expected value.3