The key components of a decision tree include decision nodes, chance nodes, branches, and payoffs. Decision nodes are points where the decision-maker must choose between different alternatives, represented by squares. Chance nodes, depicted by circles, indicate points where uncertainty is involved, and various outcomes are possible, each with an associated probability. Branches connect the nodes, representing the possible actions or outcomes of a decision, and are labeled with probabilities for chance events. Payoffs or outcomes are the results associated with each path, showing the potential benefits or costs. Together, these components help structure complex decisions by visually mapping out all possible scenarios, incorporating both the decision-maker's choices and uncertainties. This approach allows for a systematic evaluation of each alternative by calculating expected values, which helps to identify the optimal decision based on the probabilities and payoffs of different outcomes.