Risk

Risk occurs when an event is a member of a class of a large number of homogeneous events and there is fairly certain knowledge of the fre­quency of occurrence of this class of events.

Risk and insurance
For example, a firm producing bolts knows from long experience that, say, 1 percent of these bolts will be defective. It will not know whether any given bolt will be de­fective, but it will know the proportion of the total number. This knowledge can be converted into a definite cost of the firm’s operations, especially where enough cases occur within a firm. In other situations, a given loss or hazard may be large and infrequent in relation to a firm’s oper­ations (such as the risk of fire), but over a large number of firms it could be considered as a "measurable" or actuarial risk. The firms can pool their risks, or a specialized firm - an insurance company - could organize the pooling for them.

Profit and loss are the results of entrepreneurial uncertainty. Actuarial risk is converted into a cost of business operation and is not responsible for profits or losses except in so far as the actuarial estimates are wrong.

Probability
There are two types of probability, demonstrating the difference between uncertainty and risk.

Class probability means, that we know nothing about an individual outcome, but we know everything about a whole class of events, and are certain about the future. In a lottery, for example, we know how many tickets are in total and how many will be drawn. But that does not say at all, if a particular ticket or tickets will win, and buying more tickets does not increase the chance of winning. An instance of class probability is called risk. It is possible to insure against risk, because the behavior of a class of events (or a reasonable subset of it) is well known.

Case probability means, that we know some of the factors which determine the outcome of a particular event; but there are other determining factors which we don't know. The cases are individual, unique, and nonrepeatable, their result is uncertain. If in roulette a ball falls ten times on red in succession, the probability, that in the next turn will be the result black, is not greater than it was before. Football games cannot be predicted on the results of last games, nor can be presidential elections.