How do I approach Statistics & Math interview questions?

Statistics & Math questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master statistics & math interviews.

What difficulty level is this interview question?

This is a easy difficulty Statistics & Math question, commonly asked during Onsite rounds at Meta.

What role is this question designed for?

This question is commonly asked for Data Scientist candidates at Meta during technical interviews.

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

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

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

Constraints & Assumptions

Preserve the scope, facts, inputs, and requested outputs from the prompt above.
If the prompt leaves a detail unspecified, state a reasonable assumption before relying on it.
Keep the answer interview-ready: concise enough to present, but concrete enough to implement or evaluate.

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?

Quick Overview

Questions

What is the probability that an answer is both honest and relevant, P(H ∩ R)?

Given logs of 1,000 answers, how many would you expect to be neither honest nor relevant?

Describe how to run a hypothesis test to compare two LLMs’ relevance rates at significance level α = 0.05.

Constraints & Assumptions

Preserve the scope, facts, inputs, and requested outputs from the prompt above.

If the prompt leaves a detail unspecified, state a reasonable assumption before relying on it.

Keep the answer interview-ready: concise enough to present, but concrete enough to implement or evaluate.

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?

Calculate Probability of Honest and Relevant Chatbot Answers

Quick Overview

Calculate Probability of Honest and Relevant Chatbot Answers

Calculate Probability of Honest and Relevant Chatbot Answers

Chatbot Evaluation: Honesty and Relevance

Scenario

Questions

Constraints & Assumptions

Clarifying Questions to Ask Guidance

What a Strong Answer Covers Guidance

Follow-up Questions Guidance

Write your answer

Calculate Probability of Honest and Relevant Chatbot Answers

Quick Overview

Calculate Probability of Honest and Relevant Chatbot Answers

Calculate Probability of Honest and Relevant Chatbot Answers

Chatbot Evaluation: Honesty and Relevance

Scenario

Questions

Constraints & Assumptions

Clarifying Questions to Ask Guidance

What a Strong Answer Covers Guidance

Follow-up Questions Guidance

Write your answer