Chain letters. In a population of n + 1 people a man, the "progenitor," sends out letters to two distinct persons, the "first generation." These repeat the performance and, generally, for each letter received the recipient sends out two letters to two persons chosen at random without regard to the past development. Find the probability that the generations number 1, 2,..., will not include the progenitor. Find the median of the distribution, supposing n to be large.