The law of large numbers establishes convergence (in probability or almost surely, depending on which version you choose) of the sample average to the populatio

The law of large numbers establishes convergence (in probability or almost surely, depending on which version you choose) of the sample average to the population mean. This implies what you are saying but the simpler argument is just that if each /. comment has probability p > 0 of becoming infamous, then the probability of more at least one of n comments becoming infamous is 1 - (1 - p)^n -> 1.