Determine Probability of Video Selection and Impact Evaluation
Overview
This question evaluates understanding of probability and combinatorics applied to selection without replacement, complementary-event reasoning, and the ability to connect these concepts to recommendation system design and impact evaluation, falling under Statistics & Math and Data Science with relevance to recommender systems and applied machine learning. It is commonly asked to assess quantitative reasoning about ordered versus unordered selections, probabilistic complements, experimental impact on metrics, and model choice, testing both conceptual understanding of probability theory and practical application to system-level modeling.
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?
Solution
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