Compare two ad insertion strategies

A feed contains 100 posts. Strategy A: convert each post into an ad independently with probability $p = 0.04$. Strategy B: deterministically make exactly one of every 25 posts an ad (that is, exactly 4 ads, with spacing that prevents adjacency). For each strategy: (a) Compute $E[\#\text{ads}]$ and $\mathrm{Var}[\#\text{ads}]$. (b) Under Strategy A, compute $P(\#\text{ads} \ge 9)$ exactly and using a normal approximation with a continuity correction; under Strategy B, compute the same probability. (c) Under Strategy A, derive the expected number of adjacent ad pairs and approximate $P(\text{at least one adjacent ad})$ using a suitable method (for example, inclusion–exclusion or a Poisson approximation). (d) Which strategy is more likely to produce back-to-back ads, and why? Overview: This question tests a candidate's skills in probability and statistical modeling, including computing expectation and variance, binomial and normal approximations with continuity correction, Poisson or inclusion–exclusion approximations, and comparing stochastic versus deterministic experimental designs. Read the full data scientist interview experience where this question appeared.