##### Scenario Comparing two ways of inserting ads in a 100-post news feed ##### Question Option A: each post independently becomes an ad with probability 4%. Option B: exactly 1 out of every 25 posts is an ad. For each option, compute the expected number and variance of ads in 100 posts. For each option, what is the probability of showing more than twice the expected number of ads? For each option, estimate the expected count of adjacent ad pairs and determine which option is more likely to create long runs of ads. ##### Hints Use binomial moments for A, deterministic counts for B, normal tail approximation, and (n− 1)p² for adjacent-pair expectation.

This question evaluates competency in probability and statistical modeling—expectation, variance, tail probabilities, and dependence/clustering in discrete sequences—within the Statistics & Math domain.

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Statistics & Math questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master statistics & math interviews.

What difficulty level is this interview question?

This is a medium difficulty Statistics & Math question, commonly asked during Onsite rounds at Meta.

What role is this question designed for?

This question is commonly asked for Data Scientist candidates at Meta during technical interviews.

Calculate Ad Insertion Statistics for Two Methods

Scenario

Evaluating two ad-insertion strategies in a 100-post feed.

Option A (independent placement): Each post independently becomes an ad with probability p = 0.04.
Option B (quota per block): Exactly 1 out of every 25 posts is an ad.

Assumption for Option B: The total ad count is deterministic (4 ads in 100 posts). If positions are not fixed, assume 4 blocks of 25 posts; in each block, the ad’s position is chosen uniformly at random and independently across blocks. If positions are fixed (e.g., every 25th post), call that out where it affects adjacency.

Questions

For each option, compute the expected number and variance of ads in 100 posts.
For each option, compute the probability of showing more than twice the expected number of ads.
For each option, estimate the expected count of adjacent ad pairs (i.e., post i and i+1 both ads) and determine which option is more likely to create long runs of ads.

Hints: Use binomial moments for A, deterministic counts for B, normal tail approximation, and (n−1) p^2 for adjacent-pair expectation.

Scenario

Evaluating two ad-insertion strategies in a 100-post feed.

Option A (independent placement): Each post independently becomes an ad with probability p = 0.04.

Option B (quota per block): Exactly 1 out of every 25 posts is an ad.

Questions

For each option, compute the expected number and variance of ads in 100 posts.

For each option, compute the probability of showing more than twice the expected number of ads.

For each option, estimate the expected count of adjacent ad pairs (i.e., post i and i+1 both ads) and determine which option is more likely to create long runs of ads.

Hints: Use binomial moments for A, deterministic counts for B, normal tail approximation, and (n−1) p^2 for adjacent-pair expectation.

Calculate Ad Insertion Statistics for Two Methods

Quick Overview

Scenario

Questions

Solution

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Calculate Ad Insertion Statistics for Two Methods

Quick Overview

Scenario

Questions

Solution

Comments (0)