##### 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.

Meta statistics prompt comparing two ad-insertion strategies, covering binomial moments, deterministic quotas, tail probability for excessive ads, adjacent ad pairs, and risk of long ad runs.

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Calculate Ad Insertion Statistics for Two Methods

Ad Insertion Statistics for Two Feed Strategies

You are comparing two ways of inserting ads into a 100-post feed.

Option A: Each post independently becomes an ad with probability p = 0.04 .
Option B: Exactly 1 out of every 25 posts is an ad, so there are exactly 4 ads in 100 posts.

For Option B, if positions are not fixed, assume each 25-post block contains exactly one ad whose position is chosen uniformly at random and independently across blocks. If the positions are fixed, call out how that changes adjacency.

Constraints & Assumptions

Use the stated 100-post feed and 4% ad probability.
Define "more than twice the expected number" as strictly more than 8 ads.
Define an adjacent ad pair as positions i and i+1 both being ads.
Explain both expected counts and user-experience risk from variance or long runs.

Clarifying Questions to Ask

Are the exact ad positions fixed in Option B or random within each block?
Are blocks independent?
Do we care only about total ad count or also local clustering and long ad runs?

What a Strong Answer Covers

Option A ad count is Binomial(100, 0.04) with expected value 4 and variance 3.84.
Option B has deterministic total count 4 and variance 0.
Option A has a nonzero probability of more than 8 ads; Option B has probability 0.
Adjacent-pair expectation for Option A is approximately (99) * p^2 .
For random-in-block Option B, adjacency can occur mainly across block boundaries; for fixed every-25th placement it can be eliminated.
Option A is more likely to create long runs because placements are independent and unbounded locally.

Follow-up Questions

How would you compute the exact binomial tail for Option A?
Which option creates a better user experience if users dislike ad clusters?
How would you design a hybrid strategy that controls count and spacing?

Ad Insertion Statistics for Two Feed Strategies

You are comparing two ways of inserting ads into a 100-post feed.

Option A: Each post independently becomes an ad with probability p = 0.04 .

Option B: Exactly 1 out of every 25 posts is an ad, so there are exactly 4 ads in 100 posts.

Constraints & Assumptions

Use the stated 100-post feed and 4% ad probability.

Define "more than twice the expected number" as strictly more than 8 ads.

Define an adjacent ad pair as positions i and i+1 both being ads.

Explain both expected counts and user-experience risk from variance or long runs.

Clarifying Questions to Ask

Are the exact ad positions fixed in Option B or random within each block?

Are blocks independent?

Do we care only about total ad count or also local clustering and long ad runs?

What a Strong Answer Covers

Option A ad count is Binomial(100, 0.04) with expected value 4 and variance 3.84.

Option B has deterministic total count 4 and variance 0.

Option A has a nonzero probability of more than 8 ads; Option B has probability 0.

Adjacent-pair expectation for Option A is approximately (99) * p^2 .

For random-in-block Option B, adjacency can occur mainly across block boundaries; for fixed every-25th placement it can be eliminated.

Option A is more likely to create long runs because placements are independent and unbounded locally.

Follow-up Questions

How would you compute the exact binomial tail for Option A?

Which option creates a better user experience if users dislike ad clusters?

How would you design a hybrid strategy that controls count and spacing?

Calculate Ad Insertion Statistics for Two Methods

Quick Overview

Calculate Ad Insertion Statistics for Two Methods

Ad Insertion Statistics for Two Feed Strategies

Constraints & Assumptions

Clarifying Questions to Ask

What a Strong Answer Covers

Follow-up Questions

Write your answer

Calculate Ad Insertion Statistics for Two Methods

Quick Overview

Calculate Ad Insertion Statistics for Two Methods

Ad Insertion Statistics for Two Feed Strategies

Constraints & Assumptions

Clarifying Questions to Ask

What a Strong Answer Covers

Follow-up Questions

Write your answer