Expected Value Calculator

Formula first

Overview

The expected value represents the long-term average outcome of a random variable across many repetitions of an experiment. In its simplest form, it is calculated by multiplying the probability of a specific event occurring by the numerical value or payoff associated with that event.

Symbols

Variables

E = Expected Value, P = Probability, V = Value of Event

Apply it well

When To Use

When to use: Use this formula when assessing risk, making financial projections, or evaluating games of chance where outcomes are uncertain. It assumes that the probability and potential payoff are known and that the process can be reasonably averaged over time.

Why it matters: It allows decision-makers to quantify uncertainty and compare different choices on a level playing field. It serves as the mathematical foundation for modern insurance underwriting, investment portfolio management, and statistical decision theory.

Avoid these traps

Common Mistakes

• Confusing with most likely outcome.

One free problem

Practice Problem

A marketing analyst determines there is a 15% chance that a specific campaign will generate 50,000 dollars in revenue. Calculate the expected value of this specific outcome.

Solve for: $E$

Hint: Multiply the decimal probability by the total dollar amount.

The full worked solution stays in the interactive walkthrough.

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Related Formulas

References

Sources

1. Wikipedia: Expected value
2. Ross, A First Course in Probability
3. Montgomery and Runger, Applied Statistics and Probability for Engineers
4. Britannica: Expected Value
5. Ross, S. M. (2014). Introduction to Probability and Statistics for Engineers and Scientists. Academic Press.
6. Standard curriculum — GCSE Mathematics (Probability)