Two of the most frequently taught discrete probability distributions, the binomial and the hypergeometric, are presented in a comparable form that highlights both their similar structure and their distinguishing feature. Since these two random variables can equally be decomposed into sums of indicator variables, their expectations are simultaneously computed by the law of addition. That law is further utilized to simplify the calculation of the expectation of the number of runs in a random binary sequence. The same rationale is extended to two‐dimensional lattices.