Decision analysis: what does a decision tree depict to support choosing among alternatives under uncertainty?

Introduction / Context:A decision tree is a visual model to evaluate choices where outcomes are uncertain. It clarifies structure, probabilities, and payoffs, enabling expected-value or risk-sensitive comparisons.

Given Data / Assumptions:

• Alternatives exist with uncertain results.
• Probabilities and payoffs (costs/benefits) can be estimated.
• We seek what the diagram shows.

Concept / Approach:Decision nodes (squares) branch into alternatives. Chance nodes (circles) branch into outcomes with probabilities. Terminal nodes annotate consequences (payoffs). By rolling back the tree, analysts compute expected values and select a strategy.

Step-by-Step Solution:

Verification / Alternative check:Comparing expected values or applying utility functions on the same tree yields consistent strategy choices.

Why Other Options Are Wrong:Icons without logic, consequences alone, or purely equations omit the structured branching that makes trees useful.

Common Pitfalls:Ignoring dependence between branches or misestimating probabilities; always document assumptions.

Final Answer:Nodes and branches that represent decisions and chance events, plus their consequences