Ad Insertion Methods in a 100-Post Newsfeed

Context: A feed shows 100 posts to a user. The platform considers two ad-insertion schemes with the same average ad load.

• Method A (independent): Each post is replaced by an ad independently with probability p = 0.04.
• Method B (blocked): Split the feed into four blocks of 25 posts; in each block, exactly one uniformly random post is replaced by an ad (so exactly 4 ads in 100 posts).

Answer the following.

1) Expected Number of Ads

• If a user scrolls through 100 posts, what is the expected number of ads under each method?

2) Probability of Exceeding Twice the Expected Value

• What is the probability a user sees more than twice the expected number of ads (> 8) under each method?
• Compare how these probabilities differ.

3) Consecutive (Back-to-Back) Ads

• Which method is more likely to produce consecutive ads, and why?
• If you had to estimate the maximum number of consecutive ads that might appear in 100 posts, how would the methods differ in their likelihood of creating such a streak?

4) Probability of Seeing At Least One Pair of Consecutive Ads

• In 100 posts, what is the probability the user encounters at least one instance of back-to-back ads under each method?
• State any assumptions or simplifications.

5) Choosing the Better Plan

• Which plan might be more appealing from the user's perspective?
• Which plan might be more beneficial from the platform's perspective, considering risk of ad overload or clustering effects?

6) Experimental Design

• Propose an A/B test to compare the two methods in production. Include metrics such as engagement, ad impressions, CTR, and user satisfaction.