Compare Ad-Insertion Strategies: Expected Ads and Probabilities

Quick Overview

Evaluates probability, expectation, and variance for newsfeed ad-insertion strategies. Strong answers compute expected ad load, at-least-one exposure probability, and explain why equal expected counts can still produce different user experiences.

Compare Ad-Insertion Strategies: Expected Ads and Probabilities

Company: Meta

Role: Data Scientist

Category: Statistics & Math

Difficulty: easy

Interview Round: Onsite

##### Scenario Newsfeed advertising team comparing two ad-insertion strategies. ##### Question Strategy A: each post independently has 4% chance of being an ad. What is the expected number of ads in 100 posts? 2. Strategy B: exactly one ad is randomly inserted in every block of 25 posts. Compare expected ads per 100 posts. 3. Under Strategy A, what is the probability a user sees at least one ad in the next 25 posts? ##### Hints Use linearity of expectation and binomial probabilities; P(≥ 1) = 1 – (1–p)^n.

Overview: Evaluates probability, expectation, and variance for newsfeed ad-insertion strategies. Strong answers compute expected ad load, at-least-one exposure probability, and explain why equal expected counts can still produce different user experiences.

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Jul 12, 2025
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Newsfeed Ad-Insertion Strategies

You are evaluating two ways to insert ads into a user's newsfeed. A user views a contiguous sequence of posts.

  • Strategy A: each post independently has a 4% chance of being an ad.
  • Strategy B: exactly one ad is randomly inserted in every non-overlapping block of 25 posts.

Answer the questions below and explain the assumptions behind each comparison.

Constraints & Assumptions

  • Assume Strategy A uses independent Bernoulli trials with probability p = 0.04.
  • Assume the 100-post window contains exactly four complete 25-post blocks unless you explicitly discuss boundary effects.
  • Treat the user's viewed posts as the analysis window, not necessarily all posts generated by the feed.
  • Separate expected count, variance, and user experience spacing; the same expected count can still feel different.

Clarifying Questions to Ask Guidance

  • Does the 100-post window align to the start of a Strategy B block?
  • Are ads allowed to appear back-to-back under Strategy A?
  • Should we optimize only for expected ad load, or also for pacing, probability of exposure, and variance?
  • Are there minimum spacing or business rules that override the random insertion process?

Part 1 - Expected Ads in 100 Posts

Compute the expected number of ads under Strategy A and Strategy B. Compare whether the expected totals are the same.

What This Part Should Cover Guidance

  • Use linearity of expectation for the Bernoulli process in Strategy A.
  • Recognize that Strategy B is deterministic for complete 25-post blocks.
  • Explain why equal expected ad count does not imply equal variance or equal user experience.

Part 2 - Probability of at Least One Ad in 25 Posts

Under Strategy A, compute the probability that the user sees at least one ad in the next 25 posts.

What This Part Should Cover Guidance

  • Use the complement event of seeing zero ads.
  • Show the binomial expression using p = 0.04 and n = 25.
  • Interpret the result as a probability of exposure over a short viewing window.

Part 3 - Product Trade-offs

Discuss how the two strategies differ for pacing, predictability, and experimentation.

What This Part Should Cover Guidance

  • Compare variability and clustering risk under independent insertion versus block-level pacing.
  • Mention boundary effects for windows that do not align perfectly to blocks.
  • Connect the math to feed health, user irritation, advertiser delivery, and guardrail metrics.

Follow-up Questions Guidance

  • How would your answer change for a user who views only 10 posts?
  • How would you test whether Strategy B improves perceived feed quality?
  • What metrics would you monitor if the two strategies have the same expected ad load but different spacing?
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