Let p=0.62. What is the EMV associated with the decision tree?

Question

BlackTom AI · Accepted Answer

The prompt presents a question about calculating the EMV (expected monetary value) for a decision tree, given p = 0.62, but provides no answer choices or the actual tree's payoff structure.

First, recall the general approach: EMV is the sum over all possible outcomes of (probability of the outcome) × (monetary payoff of that outcome). In a decision tree, you typically propagate values from the terminal nodes upward, multiplying branch probabilities along each path and summing the weighted payoffs at splits where decisions influence the path.

Because no answer options are provided, we cannot compare candidate calculations or identify common pitfalls for incorrect choices. However, the core steps to compute EMV, once you have the tree, are:
- Identify all terminal outcomes reachable from the decision node you’re evaluating.
- For each terminal outcome, determine its probability. This often involves multiplying conditional probabilities along the path from the root to that terminal node.
- Determine the monetary payoff associated with that terminal outcome.
- Multiply the probability by the payoff for each terminal outcome and sum these products across all terminal outcomes to obtain the EMV.

If the tree includes both probabilistic events and decision branches (where you choose among options), you would:
- For chance nodes, use the given probabilities to weight outcomes.
- For decision nodes, select the action that maximizes the EMV at that node when moving backward through the tree (dynamic programming/backward induction).

With p = 0.62, you would use this probability for any outcomes whose likelihood is tied to that event. If the tree has multiple places where this probability applies, you would apply it consistently to those branches.

To proceed to a numeric EMV like 2216 (as might be indicated by the answer), you would need:
- The full set of terminal payoffs.
- The exact placement and interpretation of p = 0.62 within the tree (which branches it affects).
- Any other probabilities associated with alternative branches or outcomes.

In summary, once the decision tree is available, compute EMV by weighting each terminal payoff by its probability and summing, then, if needed, perform backward induction to account for optimal decision choices at each decision node. If you can share the full tree structure or the list of terminal payoffs with their probabilities, I can walk you through the exact calculation step by step.

COMM_V 190 101-104 2025W1 Final Exam - Practice Questions - Second Half

Let p=0.62. What is the EMV associated with the decision tree?

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