Determine Probability of Shared Videos in Recommendations
Overview
This question evaluates understanding of probability and combinatorics, specifically sampling without replacement and overlap probabilities between sets. It is commonly asked to assess quantitative reasoning about probabilistic models and product trade-offs in user engagement, falls under the Statistics & Math domain, and tests both conceptual understanding and practical application.
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Jul 12, 2025, 6:59 PM
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Statistics & Math
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Video Recommendation Probability and Product Trade-offs
Scenario
A video-recommendation system selects K distinct videos for each user from an inventory of N distinct videos (sampling without replacement per user). Two friends are each shown K videos from the same inventory. We assume selections for different users are independent (the inventory is not globally depleted across users).
Questions
- If K videos are randomly chosen from N distinct videos, what is the probability that a particular video appears in the set?
- Two friends each receive K videos (without replacement within a user) from the same inventory. What is the probability they share at least one identical video?
- Should we push identical videos to friends or diversify their feeds? Discuss expected engagement impact and trade-offs.
Hints
- Use combinations and complementary probabilities.
- Connect the calculations to user engagement reasoning.
Solution
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