Scenario: Team A wants 4 % random replacement; Team B prefers a fixed 1‑in‑25 slot. Compare expected ad counts, variance, and risk of overload. Question 1: Compare two insertion methods—4 % random vs 1‑in‑25 fixed—calculate expectation, variance, and chance of exceeding twice expectation. (Hint: binomial distribution, load smoothing)

This question evaluates a candidate's ability to model and compare randomized versus deterministic ad-insertion policies using probability and statistical concepts such as expectation, variance, and tail (overload) probabilities.

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What difficulty level is this interview question?

This is a medium difficulty Analytics & Experimentation 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.

Comparing two ad‑insertion strategies

Comparing Two Ad Insertion Methods: 4% Random vs Fixed 1-in-25

Context

You are designing an ad insertion system. In any short time bucket or session, suppose there are n eligible content slots (impressions) where an ad could be inserted.

Two teams propose different policies:

Team A: Replace each slot independently with probability p = 0.04 (4% random replacement).
Team B: Use a fixed periodic schedule of exactly 1 ad every 25 slots (a 1-in-25 slot), i.e., a deterministic pattern with period 25.

Assume buckets are contiguous sequences of n slots; when relevant, assume the starting phase of the fixed schedule is uniformly random across the 25 positions (this models arbitrary bucket alignment in production).

Task

For each method, compute in a bucket of n slots:
- Expected number of ads.
- Variance of the number of ads.
For each method, compute (or tightly bound/approximate) the probability that the number of ads in a bucket exceeds twice its expectation (risk of overload).
Briefly compare the methods in terms of expected counts, variability (load smoothing), and overload risk.

Hint: For the 4% random method, model the count of ads with a binomial distribution.

Context

You are designing an ad insertion system. In any short time bucket or session, suppose there are n eligible content slots (impressions) where an ad could be inserted.

Two teams propose different policies:

Team A: Replace each slot independently with probability p = 0.04 (4% random replacement).

Team B: Use a fixed periodic schedule of exactly 1 ad every 25 slots (a 1-in-25 slot), i.e., a deterministic pattern with period 25.

Task

For each method, compute in a bucket of n slots:

Expected number of ads.
Variance of the number of ads.

For each method, compute (or tightly bound/approximate) the probability that the number of ads in a bucket exceeds twice its expectation (risk of overload).

Briefly compare the methods in terms of expected counts, variability (load smoothing), and overload risk.

Hint: For the 4% random method, model the count of ads with a binomial distribution.

Comparing two ad‑insertion strategies

Quick Overview

Comparing Two Ad Insertion Methods: 4% Random vs Fixed 1-in-25

Context

Task

Solution

Submit Your Answer to Earn 20XP

Comparing two ad‑insertion strategies

Quick Overview

Comparing Two Ad Insertion Methods: 4% Random vs Fixed 1-in-25

Context

Task

Solution

Submit Your Answer to Earn 20XP