Compute probabilities for chatbot response quality

## 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?