Compute probabilities for chatbot response quality

Q: Compute probabilities for chatbot response quality

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.

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

Question

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

What is $P(\text{Good})$ for a single response?
What is the probability of getting two good responses in a row ?
Given the first three responses are good, what is the probability that the 4th response is good?

Compute probabilities for chatbot response quality

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Compute probabilities for chatbot response quality

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