The paper aims to represent the author’s methodological position that risk is a consequence of the decisions made by the person and is always associated with the person who not only makes a choice, but also evaluates the probabilities of possible events and associated losses. Taking a risk, the person chooses an alternative that is the result of her decision, although the possible results are not exactly known to her. The key to managing risk is the issue of measuring it. The law of large numbers by J. Bernoulli and related methodological and philosophical issues are considered. The significance of the St. Petersburg paradox for the modern understanding of risk is shown. Our thesis is that decision-making under the conditions of risk is not a person’s collision with circumstances independent of her, but a conscious and rational choice.