Short Answer

Calculating Log-Probability for a Ranked List

A model is designed to rank three candidate responses {A, B, C} for a given prompt. The model determines the final ranking by making a sequence of choices. At each step, it computes the probability of selecting the best response from the set of options not yet ranked.

Given the following conditional probabilities for the sequence A > B > C:

  • The probability of selecting A first from the set {A, B, C} is 0.5.
  • The probability of selecting B second from the remaining set {B, C} is 0.7.
  • The probability of selecting C third from the final set {C} is 1.0.

Calculate the total log-probability (using the natural logarithm, ln) for the complete ranked sequence A > B > C. Provide your final answer rounded to two decimal places and show the summation formula you used.

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Updated 2025-10-08

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