How is expected utility calculated?

Expected utility is calculated by summing the product of probabilities and total utilities for each possible state or outcome. This method integrates both the likelihood of each outcome occurring and the value or utility associated with that outcome, providing a comprehensive view of the decision-maker’s preferences in risky situations.

By calculating expected utility in this way, individuals can make informed choices when they face uncertainty. This approach reflects how individuals weigh different outcomes based on their probabilities and the level of satisfaction or utility each outcome provides. It enables a more rational decision-making process by balancing risk and reward.

The other methods mentioned do not capture this nuanced interaction between probabilities and utilities; simply adding total utility doesn't account for the likelihood of each state. Averaging probabilities alone misses the important connection to utility values, while multiplying the highest and lowest utility outcomes disregards the full range of possible outcomes and their corresponding probabilities. Thus, summing the product of probabilities and utilities is the correct and most informative approach to calculating expected utility.