##### Scenario A social media platform is experimenting with two methods of inserting ads into users' newsfeeds. When a user views 100 news stories, the platform can either: Method A: Replace each post with an ad independently at a 4% probability. Method B: Divide the feed into blocks of 25 posts and replace exactly one random post in each block with an ad. Questions 1. Expected Number of Ads If a user scrolls through 100 posts, how many ads do you expect them to see under each method? Recall that for a binomial distribution with parameters n and p, the expected value is n×p. 2. Probability of Exceeding Twice the Expected Value What is the probability that a user sees more than twice the expected number of ads under each method? Compare how these probabilities differ between Method A (random, binomially distributed) and Method B (fixed ratio in each block). 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 each method differ in its likelihood of creating such a streak? 4. Probability of Seeing At Least One Pair of Consecutive Ads In 100 posts, what is the probability that a user will encounter at least one instance of back-to-back ads under each method? Highlight any relevant assumptions or simplifications you make. 5. Choosing the Better Plan Between Method A and Method B, 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 how you would design an experiment (e.g., an A/B test) to compare the two insertion methods in a real-world scenario. Consider metrics such as user engagement, ad impressions, click-through rates, and user satisfaction.