Expected Value Calculator
Find the expected value of up to three outcomes.
Expected value is the long-run average outcome, weighting each value by its probability.
How the Math Works
The expected value calculator uses the fundamental probability formula EV = Σ(value × probability). This means you multiply each possible outcome by its likelihood of occurring, then sum all these products. For up to three outcomes, the calculation becomes: EV = (Value1 × Probability1) + (Value2 × Probability2) + (Value3 × Probability3). Each probability must be expressed as a decimal between 0 and 1, where the sum of all probabilities equals 1. The expected value represents the long-term average result if the scenario were repeated many times, making it a powerful predictive tool in probability theory.
Practical Applications
To use this calculator, first identify all possible outcomes of your situation and assign a realistic probability to each. Enter each outcome's value (whether monetary, time-related, or another measurable quantity) along with its probability as a decimal. The calculator instantly computes the expected value, helping you make data-driven decisions. This is particularly useful in business for evaluating investment opportunities, in project management for risk assessment, or in game design for balancing rewards against odds. Professional applications include financial modeling, insurance underwriting, and quality control analysis where multiple potential results must be quantified and compared.
Day-to-Day Use
In everyday life, expected value calculations help you make smarter choices about risks and rewards. When deciding whether to take a job with a variable commission structure, you can weigh potential earnings against probability of achievement. It's valuable for evaluating insurance policies—comparing premium costs to expected medical expenses based on your health profile. Students use it to assess the value of uncertain academic opportunities, while parents might apply it when deciding on education investments. Even recreational decisions like lottery tickets or casino games become clearer when you see the expected return, helping you understand when entertainment spending aligns with entertainment value rather than false hopes of wealth.
Worked example
100×0.1 + 0×0.6 + (−10)×0.3 → 7.
FAQ
Use?
Comparing bets, investments and decisions under uncertainty.