Enter the probabilities and the possible outcomes of those probabilities of two different events to calculate the expected utility.

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## Expected Utility Formula

The following formula is used to calculate the expected utility of two outcomes.

E(u) = P1(x) * Y1^{.5} + P2(x) * Y2^{.5}

- Where E(u) is the expected utility
- P1 and P2 are the probabilities of the possible outcomes
- Y1 and Y2 are the monetary values of those outcomes

## Expected Utility Definition

Expected utility is a concept used in decision theory to measure the value or desirability of different outcomes. It enables individuals to make rational choices by considering the probabilities and utilities associated with each possible outcome.

Utility refers to the subjective satisfaction or preference an individual assigns to a particular outcome. It represents the individual’s evaluation of the desirability or worthiness of that outcome.

The concept of utility acknowledges that people have different preferences and values, allowing decision-makers to quantify and compare these preferences.

The expected utility considers the probabilities of different outcomes and the utilities associated with those outcomes. It allows decision-makers to evaluate the potential outcomes of a choice by multiplying each outcome’s utility by its probability of occurring.

By summing these expected utilities across all possible outcomes,decision-makers can determine the overall expected utility of a particular choice.

Expected utility theory also aligns with the principle of rationality. It suggests that individuals should choose the option that maximizes their expected utility, as they seek to optimize their well-being or satisfaction.

## Expected Utility Example

How to calculate expected utility?

**First, determine the two possible monetary events.**For this example, we will analyze the chance of receiving a lump sum of money through a not realistic lottery. So, the two possible outcomes are someone winning $100 or winning $150.

**Next, determine the probabilities of the events.**For this example, we will say there is a 45% chance of winning 100$ and a 35% chance of winning $150.

**Finally, calculate the expected utility.**Calculate the expected utility using the formula. So E(u) = .45*100^.5 + .35*150^.5 = 8.76

## FAQ

**What is an expected utility?**

An expected utility is a measure of the sum of probabilities and possible outcomes of a set of monetary outcomes.