How do you compute the expected monetary value in decision analysis?

• A. EV = sum p_i * value_i
• B. EV = sum value_i / n
• C. EV = max_i value_i
• D. EV = sum p_i + value_i

Answer: (A)

The main idea here is to capture the average outcome you would get if you could repeat the decision many times, taking into account both how big the payoffs are and how likely each payoff is. This is why you weight each monetary outcome by its probability and then add them up. In other words, you multiply each possible value by how likely it is and sum those products. That weighted average reflects the long-run expectation for the decision.

For example, if a payoff of 100 occurs with probability 0.2 and a payoff of -20 occurs with probability 0.8, the expected monetary value is 0.2100 + 0.8(-20) = 20 - 16 = 4. This shows the average amount you’d expect per decision if you could repeat it many times.

The other approaches miss essential parts of the idea. Dividing by the number of outcomes only works when all outcomes are equally likely, which isn’t generally the case. Taking the maximum payoff ignores the probabilities entirely and looks at a single outcome instead of the average across all possibilities. Adding the probability to the value doesn’t produce a meaningful measure of expected earnings. The probability-weighted sum is the correct way to quantify the expected monetary value.