In decision analysis, what is the definition of expected value?

• A. The probability-weighted average of all possible outcomes.
• B. The most probable single outcome.
• C. The average of observed outcomes.
• D. The maximum possible payoff.

Answer: (A)

The expected value is the probability-weighted average of all possible outcomes. It combines how big each outcome could be with how likely it is, giving a single number that represents the long-run average payoff if you could repeat the decision many times. You compute it by multiplying each possible outcome by its probability and then adding those products together.

For example, if a gamble pays $100 with probability 0.5 and loses $20 with probability 0.5, the expected value is 0.5×100 + 0.5×(-20) = 40. This means, on average, you would gain $40 per play in the long run.

This is different from the most probable single outcome (the mode), which just tells you the single likely result, not the long-run average. It’s also different from the simple average of observed outcomes, which is an empirical estimate of the expected value that improves with more data. And it differs from the maximum possible payoff, which is just the best-case scenario and says nothing about likelihood or typical results.

In decision analysis, choosing actions with the highest expected value aligns with a risk-neutral view, emphasizing averages over time. But keep in mind that expected value doesn’t capture risk preferences; sometimes a decision maker might favor a lower expected value with less risk, or adjust for uncertainty using other criteria.