The expected value of an uncertain quantity is the probability-weighted average of all its possible values:
For a project whose PW might be $5,000 (probability 20%), $10,000 (probability 50%), or $15,000 (probability 30%):
Expected value is the simplest summary of risky outcomes — and the standard one used inside decision trees to fold back chance nodes.
Interpretation. EV is the average across many independent repetitions of the same decision. If you faced this project a thousand times with these probabilities, your average PW would be very close to $10,500. For a one-off decision the actual result will be one of the three values, not the EV — but EV is still the right summary if you have no reason to weight any outcome differently.
Limits.
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Risk aversion. A decision-maker may rationally prefer a certain $8,000 over the same EV $10,500 if it spans $5k to $15k — they’d rather avoid the downside. EV doesn’t capture this preference. The fix is to use a utility function (replace dollar payoffs with the decision-maker’s utility) and maximise expected utility instead. Beyond Engineering Economics scope.
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Catastrophic downside. EV treats a 1% chance of $-1 million as roughly equivalent to a 50% chance of $-20,000 — the products are the same. But in practice, a low-probability catastrophic outcome (bankruptcy, regulatory shutdown) may matter much more than a small chance of a moderate loss. The fix is to combine EV with separate analysis of the worst-case (a sensitivity or stress-test approach).
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Probability estimates. EV is only as good as the probabilities. Made-up probabilities give made-up EVs. Be honest about the source of probabilities; in many engineering contexts, ranges or scenarios are more defensible than point probabilities.
For use in tree analysis see decision tree. For probability-free risk methods see Sensitivity analysis and Break-even analysis. For the broader context see Risk and uncertainty.