Calculate Ad Insertion Statistics for Two Methods

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.