In a population of n+1 people a man, the 'progenitor', sends out letters to two persons, the "first generation". These repeat the performance and, generally, each member of the rth generation sends out letters to two persons chosen at random. I want to find the probability that generations number 1,2,...,r will not include the progenitor. I want to find a median of the distribution, supposing n to be large.
Answer: My answer is not matching with the answer provided.My answer is $(1-\frac2n)^{2^r}$. Whereas answer given is $(1-\frac2n)^{2^r-2}$.
How to find median of this distribution?