Compare two ad insertion strategies

Quick Overview

This question evaluates a candidate's competency in probability and statistical modeling, including computation of expectation and variance, binomial and normal approximations with continuity correction, Poisson or inclusion–exclusion approximations, and comparison of stochastic versus deterministic experimental designs.

Compare two ad insertion strategies

Company: Meta

Role: Data Scientist

Category: Analytics & Experimentation

Difficulty: medium

Interview Round: Onsite

A feed shows 100 posts. Strategy A: independently turn each post into an ad with probability p = 0.04. Strategy B: deterministically make exactly one out of every 25 posts an ad (i.e., exactly 4 ads, spacing prevents adjacency). For each strategy: (a) Compute E[# ads] and Var[# ads]. (b) Under Strategy A, compute P(# ads ≥ 9) exactly and via a normal approximation with continuity correction; under Strategy B, compute the same probability. (c) Under Strategy A, derive the expected number of adjacent ad pairs and approximate P(at least one adjacent ad) using an appropriate method (e.g., inclusion–exclusion or Poisson approximation). (d) Which strategy is more likely to create back-to-back ads and why?

Quick Answer: This question evaluates a candidate's competency in probability and statistical modeling, including computation of expectation and variance, binomial and normal approximations with continuity correction, Poisson or inclusion–exclusion approximations, and comparison of stochastic versus deterministic experimental designs.

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Oct 13, 2025, 9:49 PM
mediumData ScientistOnsiteAnalytics & Experimentation
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Ad Insertion Strategies for a 100-Post Feed

You are evaluating two ad-insertion strategies on a feed with 100 posts:

  • Strategy A (Stochastic): Independently convert each post into an ad with probability p = 0.04.
  • Strategy B (Deterministic): Insert exactly 1 ad in every block of 25 posts (exactly 4 ads total in 100 posts), with spacing that prevents any two ads from being adjacent.

Answer the following:

(a) Compute the expected number of ads and the variance of the number of ads for each strategy.

(b) Compute P(# ads ≥ 9) under each strategy. For Strategy A, provide both the exact binomial expression and a normal approximation with continuity correction.

(c) Under Strategy A, compute the expected number of adjacent ad pairs (i.e., consecutive ads). Then approximate P(at least one adjacent ad) using a suitable method (e.g., inclusion–exclusion or a Poisson approximation).

(d) Which strategy is more likely to create back-to-back ads, and why?

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