Final answer:
The probabilistic decision rule that becomes possible when probabilities can be assigned to various events is known as the expected value criterion. It's used to calculate the average expected outcome based on the probability and associated value of potential events in decision-making under uncertainty.
Step-by-step explanation:
When the decision-maker is able to assign probabilities to the various events, the use of probabilistic decision rule, called the expected value criterion, becomes possible. The expected value is a key concept in decision-making under uncertainty and involves calculating the average payoff when the future includes scenarios that may or may not happen. This calculation takes into account both the probability of each scenario and the reward or loss associated with it.
The expected value is determined by summing the products of the probabilities of occurrence and the corresponding values of the outcomes. In situations where states or businesses have to decide on a course of action based on uncertain events, they often use expected value as a basis for their decision. It is a core concept in probability and statistics used to predict outcomes across various fields, including finance, insurance, economics, and game theory.