##### Scenario Designing a video-recommendation push system: selecting k videos from a large inventory and evaluating product impact between friends. ##### Question a) From an inventory of N videos, what is the probability a specific ordered set of k videos is pushed to a user? What about any unordered subset of size k? b) Given an event’s probability, compute its complementary probability and apply it to the video-selection context. c) Should we push the same video to two friends or different videos? Discuss pros, cons, and expected metrics impact. d) Which statistical or machine-learning model would you use for this recommendation problem and why? ##### Hints Use permutation/combination formulas, complementary events, discuss CTR vs. content diversity, and mention models like collaborative filtering or sequence models.

This interview question evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer for Determine Probability of Video Selection and Impact Evaluation states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

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

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

Determine Probability of Video Selection and Impact Evaluation

Video Recommendation Push: Selection Probabilities, Complements, and Design Choices

Scenario

You are designing a push-notification system that recommends k videos to a user from a large catalog of N videos. You also need to reason about whether to push the same or different videos to two friends and how to model this recommendation problem.

Assumption (unless otherwise stated): The system selects k distinct videos without replacement. If order is relevant (e.g., top-1, top-2, …), we treat the result as an ordered list; otherwise as an unordered set.

Questions

a) From an inventory of N videos, what is the probability that a specific ordered set of k distinct videos is pushed to a user? What about any specific unordered subset of size k?

b) Given an event’s probability p, compute its complementary probability and apply it to the video-selection context (e.g., the probability that at least one of a set of m target videos appears in the k selected videos).

c) For two friends, should we push the same video to both or different videos? Discuss pros, cons, and expected impact on metrics.

d) Which statistical or machine-learning model(s) would you use for this recommendation problem and why?

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?