Which statement accurately describes the relationship between probability and utility in decision trees?

• A. They are probability and utility
• B. They are both costs
• C. They are only probabilities
• D. They are only utility values

Answer: (C)

In decision trees, probability and utility are two distinct quantities that work together to evaluate choices. Probability measures how likely each outcome is, while utility represents the value or desirability of that outcome. To decide among options, you combine them by calculating the expected utility: multiply the probability of each outcome by its utility and sum across all outcomes. This weighting of utilities by their likelihood is what lets you compare strategies on a consistent scale.

Because the outcomes and their desirability are both important, the relationship isn’t that they’re the same thing or that one is the sole focus. If you only looked at probabilities, you’d ignore how good or bad each outcome is; if you only looked at utilities, you wouldn’t account for how likely those outcomes are. The key idea is that probabilities weight utilities to produce a single metric for comparison. For example, if there’s a 60% chance of a high-utility payoff and a 40% chance of a low-utility payoff, the decision hinges on the resulting expected utility, not on probabilities alone.