Compute probabilities for chatbot response quality
Company: Meta
Role: Data Scientist
Category: Statistics & Math
Difficulty: easy
Interview Round: Onsite
## Context
A chatbot response is considered **good** if it is both:
- **Helpful**, and
- **Honest**.
You are told:
- \(P(\text{Helpful}) = 0.8\)
- \(P(\text{Honest}) = 0.9\)
Assume (unless you explicitly state otherwise) that helpfulness and honesty are independent for a given response, and that responses across turns are i.i.d.
## Questions
1. What is \(P(\text{Good})\) for a single response?
2. What is the probability of getting **two good responses in a row**?
3. Given the **first three** responses are good, what is the probability that the **4th** response is good?
Quick Answer: This question evaluates a candidate's grasp of basic probability concepts, including independence, joint event probabilities, and i.i.d. assumptions. It is commonly asked to test probabilistic reasoning about repeated trials within the Statistics & Math domain and is primarily a conceptual understanding problem with a simple practical application.