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 defined as the measure of the sum of probabilities and potential outcomes of a set of monetary events.

## 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 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.