{"blocks":[{"key":"fofae","text":"Scenario","type":"header-two","depth":0,"inlineStyleRanges":[],"entityRanges":[],"data":{}},{"key":"7khk7","text":"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:","type":"unstyled","depth":0,"inlineStyleRanges":[],"entityRanges":[],"data":{}},{"key":"ks0v","text":"Method A: Replace each post with an ad independently at a 4% probability.","type":"unordered-list-item","depth":0,"inlineStyleRanges":[],"entityRanges":[],"data":{}},{"key":"c6k4t","text":"Method B: Divide the feed into blocks of 25 posts and replace exactly one random post in each block with an ad.","type":"unordered-list-item","depth":0,"inlineStyleRanges":[],"entityRanges":[],"data":{}},{"key":"4utdb","text":"Questions","type":"header-two","depth":0,"inlineStyleRanges":[],"entityRanges":[],"data":{}},{"key":"2219f","text":"1. Expected Number of Ads","type":"header-three","depth":0,"inlineStyleRanges":[],"entityRanges":[],"data":{}},{"key":"e8dut","text":"If a user scrolls through 100 posts, how many ads do you expect them to see under each method?","type":"unordered-list-item","depth":0,"inlineStyleRanges":[],"entityRanges":[],"data":{}},{"key":"17n31","text":"Recall that for a binomial distribution with parameters n and p, the expected value is n×p.","type":"unordered-list-item","depth":0,"inlineStyleRanges":[],"entityRanges":[],"data":{}},{"key":"dis46","text":"2. Probability of Exceeding Twice the Expected Value","type":"header-three","depth":0,"inlineStyleRanges":[],"entityRanges":[],"data":{}},{"key":"d5li6","text":"What is the probability that a user sees more than twice the expected number of ads under each method?","type":"unordered-list-item","depth":0,"inlineStyleRanges":[],"entityRanges":[],"data":{}},{"key":"3b49a","text":"Compare how these probabilities differ between Method A (random, binomially distributed) and Method B (fixed ratio in each block).","type":"unordered-list-item","depth":0,"inlineStyleRanges":[],"entityRanges":[],"data":{}},{"key":"cutep","text":"3. Consecutive (Back-to-Back) Ads","type":"header-three","depth":0,"inlineStyleRanges":[],"entityRanges":[],"data":{}},{"key":"1gap1","text":"Which method is more likely to produce consecutive ads, and why?","type":"unordered-list-item","depth":0,"inlineStyleRanges":[],"entityRanges":[],"data":{}},{"key":"6uift","text":"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?","type":"unordered-list-item","depth":0,"inlineStyleRanges":[],"entityRanges":[],"data":{}},{"key":"d6hst","text":"4. Probability of Seeing At Least One Pair of Consecutive Ads","type":"header-three","depth":0,"inlineStyleRanges":[],"entityRanges":[],"data":{}},{"key":"173mr","text":"In 100 posts, what is the probability that a user will encounter at least one instance of back-to-back ads