Calculate Probability of Honest and Relevant Chatbot Answers

Quick Overview

Calculate Probability of Honest and Relevant Chatbot Answers evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

Calculate Probability of Honest and Relevant Chatbot Answers

Company: Meta

Role: Data Scientist

Category: Statistics & Math

Difficulty: easy

Interview Round: Onsite

##### Scenario Evaluating a customer-service chatbot: P(honest answer)=0.7, P(relevant answer)=0.8. ##### Question What is the probability that an answer is both honest and relevant if the two events are independent? Given logs of 1,000 answers, how many would you expect to be neither honest nor relevant? Describe how you would run a hypothesis test to compare two LLMs’ relevance rates at α=0.05. ##### Hints Basic probability rules; two-proportion z-test setup and interpretation.

Overview: Calculate Probability of Honest and Relevant Chatbot Answers evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

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Aug 4, 2025
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Calculate Probability of Honest and Relevant Chatbot Answers

Chatbot Evaluation: Honesty and Relevance

Scenario

You are evaluating a customer-service chatbot. Define two events for any given answer:

  • H: the answer is honest, with P(H) = 0.7
  • R: the answer is relevant, with P(R) = 0.8 Assume H and R are independent.

Questions

  1. What is the probability that an answer is both honest and relevant, P(H ∩ R)?
  2. Given logs of 1,000 answers, how many would you expect to be neither honest nor relevant?
  3. Describe how to run a hypothesis test to compare two LLMs’ relevance rates at significance level α = 0.05.

Clarifying Questions to Ask Guidance

  • Clarify the random variables, distributional assumptions, independence assumptions, and desired output.
  • Show enough derivation for the interviewer to follow the reasoning.
  • Explain how you would validate the result with simulation or sensitivity checks.

What a Strong Answer Covers Guidance

  • A correct setup with definitions, formulas, and boundary conditions.
  • A step-by-step derivation or estimation plan.
  • Interpretation of the result, including uncertainty and practical limitations.
  • Checks for assumptions, edge cases, and numerical stability.

Follow-up Questions Guidance

  • How would the result change if the assumptions were relaxed?
  • Can you verify the answer with a simulation?
  • What is the most likely source of estimation error?
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