The Doomsday argument is a probability-based argument that predicts that there is a 95% probability that the human race will go extinct within the next 9120 years. The argument assumes that out of the total number of humans that will ever be born in the past or future, at least 5% have already been born. Then, using predictions for future birthrates, population, and lifespan, it calculates the number 9120 as an upper bound the number of years it will take for the remaining humans to be born and die, assuming we are in the last 95% of humans ever to be born. Wikipedia has a much better explanation of it.