Decision trees: what do they depict and how are they structured for analyzing choices and outcomes?

Introduction / Context:
Decision trees visualize decisions under uncertainty. They help compare alternatives by laying out conditions, choices, probabilities, and payoffs in a clear, analyzable structure. They are widely used in systems design trade-offs, project risk analysis, and classification models.

Given Data / Assumptions:

• We need a tool that shows choices and subsequent outcomes.
• We value a structure that is both visual and analyzable.
• We may attach probabilities and costs/benefits to outcomes.

Concept / Approach:
Decision trees consist of nodes (decision nodes, chance nodes, terminal nodes) connected by branches that represent options and events. Consequences (e.g., cost, time, payoff) are associated with terminal nodes, enabling expected value calculations. The pictorial form makes scenario exploration and stakeholder discussion straightforward.

Step-by-Step Solution:
Identify components: nodes (squares/diamonds/circles by convention) and branches.Map conditions and choices to branches emanating from nodes.Annotate outcomes with consequences (payoff, loss, time, risk).Compute expected values where probabilities are known to compare alternatives.

Verification / Alternative check:
When used in feasibility decisions, trees allow “roll-back” analysis: compute expected values from the leaves back to the root, selecting the branch with the highest expected benefit or lowest expected cost.

Why Other Options Are Wrong:
Each of A, B, and C describes an essential aspect; therefore, the composite answer “All of the above” is correct. “None” is false because decision trees indeed use these elements.

Common Pitfalls:
Ignoring correlated risks, double-counting probabilities, or omitting significant branches; ensure trees are comprehensive yet tractable.

Final Answer:
All of the above