Why does the probability of heads not predict the result of one particular coin toss?
Swiss commemorative stamp of mathematician Jakob Bernoulli, issued 1994, displaying the formula and the graph for the law of large numbers, first proved by Bernoulli in 1713.
The probability of heads does not predict the result of a single coin toss because probability theory describes the long-term frequency of outcomes in repeated experiments, not the certainty of any individual trial.12
When you toss a coin, the sample space consists of two equally likely outcomes: heads or tails. While the theoretical probability of heads is 1/2, this value represents the ratio of favorable outcomes to the total number of possible outcomes over many trials.2
The law of large numbers explains that as the number of independent trials increases, the observed fraction of heads will approach the theoretical probability. However, this law does not imply that a "shortfall" of heads in early tosses must be corrected by future results; each individual toss remains an independent event with its own inherent uncertainty. Therefore, while probability allows us to analyze patterns across large datasets, it cannot determine the specific outcome of one particular toss.12