Suppose that the decisionmaker takes the personal retreat. For some values of p and q, suppose that the payoff associated with decision H is 258.2 if she senses consolation, and the payoff associated with decision H is 165.8 if she senses desolation. What is the payoff associated with sensing consolation in a decision tree corresponding to the decisionmaker's problem? (Choose the most correct answer.)

Question

Suppose that the decisionmaker takes the personal retreat. For some values of p and q, suppose that the payoff associated with decision H is 258.2 if she senses consolation, and the payoff associated with decision H is 165.8 if she senses desolation. What is the payoff associated with sensing consolation in a decision tree corresponding to the decisionmaker's problem?  (Choose the most correct answer.)

BlackTom AI · Accepted Answer

First, let’s restate the question and all answer options to ensure clarity. The problem states: For some values of p and q, the payoff for decision H is 258.2 if consolation is sensed, and 165.8 if desolation is sensed. What is the payoff associated with sensing consolation in the decision tree? (Choose the most correct answer.)

Option 1: "258.2 since it is greater than 165.8". This option asserts that the consolation payoff is 258.2 and justifies it by noting that 258.2 exceeds 165.8. Since the consolation payoff is explicitly given as 258.2 when consolation is sensed, this option correctly states the value and uses a straightforward comparison to the desolation payoff to support why it is the consolation payoff rather than the desolation payoff.

Option 2: "165.8 since it is smaller than 258.2". This option identifies 165.8 as the payoff for sensing consolation, but the problem states that 165.8 is the payoff for sensing desolation, not for consolation. Therefore this choice confuses the two possible states and is incorrect.

Option 3: "None listed here". This would be correct only if none of the provided statements matched the payoff, but at least one option correctly states the consolation payoff, so this is not appropriate.

Option 4: "258.2 since it is greater than 200.". While it is true that 258.2 is greater than 200, using this threshold to justify the consolation payoff is extraneous and not the direct basis given in the problem. The payoff is defined by the consolation state as 258.2 regardless of comparison to 200, so this justification is weak and not the most direct explanation.

Option 5: "A number between 165.8 and 258 (a \"sumproduct\" of these two numbers)". This suggests a value that blends the two payoffs, which does not align with the problem’s specification that the consolation payoff is exactly 258.2 when consolation is sensed. This is neither the stated value nor a reasonable interpretation of the provided payoffs.

To summarize the reasoning across options: the problem gives explicit payoffs for the two sensing states—258.2 for consolation and 165.8 for desolation. The direct and correct interpretation is that the consolation payoff is 258.2. Any justification that relies on comparing the two payoffs (as in options 1 and 2) hinges on the known values, but option 1 directly aligns with the problem’s explicit statement, whereas option 4 relies on an arbitrary threshold (200) that is not part of the payoff definition, and option 5 suggests an implausible blended value. The phrasing in option 3 would only be correct if no option matched, which is not the case here, and option 2 reverses the states, assigning the desolation payoff to consolation.

COMM_V 190 101-104 2025W1 2025W1 COMM 190 Final Exam - TUE Dec 09 2025 - Requires Respondus LockDown Browser

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